Theorem ifpnancor

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

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

Proof

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