Theorem ifpancor 37808

Description: Corollary of commutation of and. (Contributed by RP, 25-Apr-2020.)

Assertion

Ref	Expression
ifpancor	|- (if- ( ph , ps , ph ) <-> if- ( ps , ph , ps ) )

Proof of Theorem ifpancor

Step	Hyp	Ref	Expression
1		ancom 466	. 2 |- ( ( ph /\ ps ) <-> ( ps /\ ph ) )
2		ifpdfan2 37807	. 2 |- ( ( ph /\ ps ) <-> if- ( ph , ps , ph ) )
3		ifpdfan2 37807	. 2 |- ( ( ps /\ ph ) <-> if- ( ps , ph , ps ) )
4	1, 2, 3	3bitr3i 290	1 |- (if- ( ph , ps , ph ) <-> if- ( ps , ph , ps ) )

Syntax hints:   <-> wb 196   /\ wa 384  if-wif 1012

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8

This theorem depends on definitions:  df-bi 197  df-or 385  df-an 386  df-ifp 1013

This theorem is referenced by:  ifpnancor  37826