Theorem ifporcor 37806

Description: Corollary of commutation of or. (Contributed by RP, 20-Apr-2020.)

Assertion

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

Proof of Theorem ifporcor

Step	Hyp	Ref	Expression
1		orcom 402	. 2 |- ( ( ph \/ ps ) <-> ( ps \/ ph ) )
2		ifpdfor2 37805	. 2 |- ( ( ph \/ ps ) <-> if- ( ph , ph , ps ) )
3		ifpdfor2 37805	. 2 |- ( ( ps \/ ph ) <-> if- ( ps , ps , ph ) )
4	1, 2, 3	3bitr3i 290	1 |- (if- ( ph , ph , ps ) <-> if- ( ps , ps , ph ) )

Syntax hints:   <-> wb 196   \/ wo 383  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:  ifpnorcor  37825