Theorem im2anan9r 809

Description: Deduction joining nested implications to form implication of conjunctions. (Contributed by NM, 29-Feb-1996.)

Hypotheses

Ref	Expression
im2an9.1	|- (ph -> (ps -> ch))
im2an9.2	|- (th -> (ta -> et))

Assertion

Ref	Expression
im2anan9r	|- ((th /\ ph) -> ((ps /\ ta) -> (ch /\ et)))

Proof of Theorem im2anan9r

Step	Hyp	Ref	Expression
1		im2an9.1	. . 3 |- (ph -> (ps -> ch))
2		im2an9.2	. . 3 |- (th -> (ta -> et))
3	1, 2	im2anan9 808	. 2 |- ((ph /\ th) -> ((ps /\ ta) -> (ch /\ et)))
4	3	ancoms 439	1 |- ((th /\ ph) -> ((ps /\ ta) -> (ch /\ et)))

This proof depends on syntax axioms:   -> wi 4   /\ wa 358

This proof depends on axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8

This proof depends on definitions:  df-bi 177  df-an 360

This theorem is used by: (None)