Theorem ifpdfan2

Description: Define and with conditional logic operator. (Contributed by RP, 25-Apr-2020)

	Ref	Expression
Assertion	ifpdfan2	|- ( ( ph /\ ps ) <-> if- ( ph , ps , ph ) )

Proof

Step	Hyp	Ref	Expression
1		id	|- ( ph -> ph )
2	1	notnoti	|- -. -. ( ph -> ph )
3	2	biorfi	|- ( ( ph /\ ps ) <-> ( ( ph /\ ps ) \/ -. ( ph -> ph ) ) )
4		dfifp6	|- ( if- ( ph , ps , ph ) <-> ( ( ph /\ ps ) \/ -. ( ph -> ph ) ) )
5	3 4	bitr4i	|- ( ( ph /\ ps ) <-> if- ( ph , ps , ph ) )