In Matthew 10:40-42, Jesus uses what's called a hypothetical syllogism. The logical form of the argument is:
1. If A then B.
2. B then C.
3. Therefore, if A then C.
He doesn't actually state the conclusion explicitly. Whether that's because he wanted his hearers to draw it themselves, or whether it's because Matthew has eclipsed the account as he often does, is irrelevant. In the Matthew account it's clearly implied, so Jesus need not have stated it to intend the argument to take this form. It's a pretty straightforward argument: "He who receives you receives me, and he who receives me receives the one who sent me." (Matthew 10:40, NIV)
The logical form is as follows:
1. If someone receives you, that person is receiving me.
2. If someone receives me, that person is receiving the one who sent me.
3. Implied conclusion: If someone receives you, that person is receiving the one who sent me.
Jesus' disciples are being sent out to preach that the kingdom of heaven is near and to perform miracles as evidence of that claim. In context, receiving someone amounts to taking in disciples and receiving their message. As he summarizes Jesus' pep talk before sending them out, Matthew focuses in for a bit on some of Jesus' teachings on how people will respond differently to them. One of the things he's been saying in this section is that acceptance of him amounts to acceptance of his Father, and acceptance of those who follow him is acceptance of him. He hasn't said it in so many words, but a careful digestion of the sort of thing he's getting at will lead to that implication.
In v.32, he says, "Whoever acknowledges me before men, I will also acknowledge before my Father in heaven. But whoever disowns me before men, I will disown him before my Father in heaven." This doesn't quite amount to saying that the person receiving them receives him, but it does say that the Father's view of it is as if he is as connected with it as they are. Even earlier, in v.20, he said that their speaking is really the Spirit of their Father speaking through them. Then vv. 24-25 point out that they will be treated as he is treated by those who hate him. None of this amounts to explicit connecting of premises and conclusions, but what he's doing is suggestive of what you might do if you were to draw those out. He states all that earlier, and now he's coming back to enable those paying attention to draw the obvious conclusion.
The other element he brings out comes after the syllogism, as if to explain its significance further. You receive a prophet's reward if you receive a prophet, and you receive a righteous man's reward if you receive a righteous man. What kind of reward, then, will someone receiving one of Jesus' disciples receive? Here's an a fortiori argument, one of Jesus' most common argument forms (probably second only to his extremely frequent arguments from analogy, a category which would include his parables). If the reward for receiving someone who is only a prophet gets a prophet's reward, and receiving someone who is only a righteous man gets a righteous man's reward, what will it mean to receive someone when receiving that person amounts to receiving God? There's a lot more to this syllogism than the simple form of it would indicate.