Theorem ancom2s 487

Description: Inference commuting a nested conjunction in antecedent.

Hypothesis

Ref	Expression
an1s.1	|- ((ph /\ (ps /\ ch)) -> th)

Assertion

Ref	Expression
ancom2s	|- ((ph /\ (ch /\ ps)) -> th)

Proof of Theorem ancom2s

Step	Hyp	Ref	Expression
1		an1s.1	. . . 4 |- ((ph /\ (ps /\ ch)) -> th)
2	1	exp32 377	. . 3 |- (ph -> (ps -> (ch -> th)))
3	2	com23 32	. 2 |- (ph -> (ch -> (ps -> th)))
4	3	imp32 363	1 |- ((ph /\ (ch /\ ps)) -> th)

Syntax hints:   -> wi 3   /\ wa 223

This theorem is referenced by:  fr2nr 2925  xpexr2 3480  isowe 3903  mulsubt 5477  leltaddt 5646  znnen 7502  metcnpi3 7892  iscau3 7938  iscau4 7940  irredlem2 10318

This theorem was proved from axioms:  ax-1 4  ax-2 5  ax-3 6  ax-mp 7

This theorem depends on definitions:  df-bi 147  df-an 225

Copyright terms: Public domain