Theorem dfifp3

Description: Alternate definition of the conditional operator for propositions. (Contributed by BJ, 30-Sep-2019)

	Ref	Expression
Assertion	dfifp3	|- ( if- ( ph , ps , ch ) <-> ( ( ph -> ps ) /\ ( ph \/ ch ) ) )

Proof

Step	Hyp	Ref	Expression
1		dfifp2	|- ( if- ( ph , ps , ch ) <-> ( ( ph -> ps ) /\ ( -. ph -> ch ) ) )
2		pm4.64	|- ( ( -. ph -> ch ) <-> ( ph \/ ch ) )
3	2	anbi2i	|- ( ( ( ph -> ps ) /\ ( -. ph -> ch ) ) <-> ( ( ph -> ps ) /\ ( ph \/ ch ) ) )
4	1 3	bitri	|- ( if- ( ph , ps , ch ) <-> ( ( ph -> ps ) /\ ( ph \/ ch ) ) )