Theorem ifpbicor

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

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

Proof

Step	Hyp	Ref	Expression
1		bicom	|- ( ( ph <-> ps ) <-> ( ps <-> ph ) )
2		ifpdfbi	|- ( ( ph <-> ps ) <-> if- ( ph , ps , -. ps ) )
3		ifpdfbi	|- ( ( ps <-> ph ) <-> if- ( ps , ph , -. ph ) )
4	1 2 3	3bitr3i	|- ( if- ( ph , ps , -. ps ) <-> if- ( ps , ph , -. ph ) )