Theorem ifpbi23d

Description: Equivalence deduction for conditional operator for propositions. Convenience theorem for a frequent case. (Contributed by Wolf Lammen, 28-Apr-2024)

	Ref	Expression
Hypotheses	ifpbi23d.1	|- ( ph -> ( ch <-> et ) )
	ifpbi23d.2	|- ( ph -> ( th <-> ze ) )
Assertion	ifpbi23d	|- ( ph -> ( if- ( ps , ch , th ) <-> if- ( ps , et , ze ) ) )

Proof

Step	Hyp	Ref	Expression
1		ifpbi23d.1	|- ( ph -> ( ch <-> et ) )
2		ifpbi23d.2	|- ( ph -> ( th <-> ze ) )
3		biidd	|- ( ph -> ( ps <-> ps ) )
4	3 1 2	ifpbi123d	|- ( ph -> ( if- ( ps , ch , th ) <-> if- ( ps , et , ze ) ) )