Theorem ifpbicor 37820

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

Assertion

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

Proof of Theorem ifpbicor

Step	Hyp	Ref	Expression
1		bicom 212	. 2 |- ( ( ph <-> ps ) <-> ( ps <-> ph ) )
2		ifpdfbi 37818	. 2 |- ( ( ph <-> ps ) <-> if- ( ph , ps , -. ps ) )
3		ifpdfbi 37818	. 2 |- ( ( ps <-> ph ) <-> if- ( ps , ph , -. ph ) )
4	1, 2, 3	3bitr3i 290	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:  ifpxorcor  37821