Theorem ancomsd 335

Description: Deduction commuting conjunction in antecedent.

Hypothesis

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

Assertion

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

Proof of Theorem ancomsd

Step	Hyp	Ref	Expression
1		ancomsd.1	. 2 |- (ph -> ((ps /\ ch) -> th))
2		ancom 333	. 2 |- ((ch /\ ps) <-> (ps /\ ch))
3	1, 2	syl5ib 181	1 |- (ph -> ((ch /\ ps) -> th))

Syntax hints:   -> wi 2   /\ wa 196

This theorem is referenced by:  sylan2d 353  anabsi6 378  fr2nr 2177  cfub 3703  cvcon3t 5716  atexch 5769

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

This theorem depends on definitions:  df-bi 128  df-an 198

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