If B then C, thus if (A and B) then C

>If B then C, thus if (A and B) then C

Why the fuck can;t I wrap my mind around this? Can anyone do a proof?

(A and B) then B
B then C

How is (A and B) then B logical?

Maybe I'm just dumb but let me give this a shot:

(A and B) is the intersection between A and B so it is a subset of both A and B. So anything in (A and B) is also in B. So we can say if B then C, thus if subset(B) then C as an equivalent expression

If we know both A and B are true statements, then we know (trivially) that B is a true statement.
If we know Adam and Bill are humans, then we know Bill is a human.

You made that way more confusing than it needed to be.

>>If B then C, thus if (A and B) then C
How about this:
A = has brown hair
B = is human
C = has two legs

(A and B) describes an object which is both human and has brown hair. Therefore said object has two legs

I think you got this OP but

A AND B means A = 1, B =1

B =1 then C = 1

thus

A and B then C

And vs or is the key kohai

If B is a true statement, then C is a true statement.

A's truthness is unrelated to C's. So if A = true AND B = true, we know that C = is true because the statement that matters (B) is true.