Theorem ifpxorcor 37821

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

Assertion

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

Proof of Theorem ifpxorcor

Step	Hyp	Ref	Expression
1		ifpbicor 37820	. 2 |- (if- ( ph , -. ps , -. -. ps ) <-> if- ( -. ps , ph , -. ph ) )
2		notnotb 304	. . 3 |- ( ps <-> -. -. ps )
3		ifpbi3 37812	. . 3 |- ( ( ps <-> -. -. ps ) -> (if- ( ph , -. ps , ps ) <-> if- ( ph , -. ps , -. -. ps ) ) )
4	2, 3	ax-mp 5	. 2 |- (if- ( ph , -. ps , ps ) <-> if- ( ph , -. ps , -. -. ps ) )
5		ifpn 1022	. 2 |- (if- ( ps , -. ph , ph ) <-> if- ( -. ps , ph , -. ph ) )
6	1, 4, 5	3bitr4i 292	1 |- (if- ( ph , -. ps , ps ) <-> if- ( ps , -. ph , ph ) )

Syntax hints:   -. wn 3   <-> wb 196  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  df-tru 1486

This theorem is referenced by: (None)