Theorem ifpnancor 37826

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

Assertion

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

Proof of Theorem ifpnancor

Step	Hyp	Ref	Expression
1		ifpancor 37808	. . 3 |- (if- ( ph , ps , ph ) <-> if- ( ps , ph , ps ) )
2	1	notbii 310	. 2 |- ( -. if- ( ph , ps , ph ) <-> -. if- ( ps , ph , ps ) )
3		ifpnot23 37823	. 2 |- ( -. if- ( ph , ps , ph ) <-> if- ( ph , -. ps , -. ph ) )
4		ifpnot23 37823	. 2 |- ( -. if- ( ps , ph , ps ) <-> if- ( ps , -. ph , -. ps ) )
5	2, 3, 4	3bitr3i 290	1 |- (if- ( ph , -. ps , -. ph ) <-> if- ( ps , -. ph , -. ps ) )

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

This theorem is referenced by: (None)