Metamath Proof Explorer


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 φχη
ifpbi23d.2 φθζ
Assertion ifpbi23d φif-ψχθif-ψηζ

Proof

Step Hyp Ref Expression
1 ifpbi23d.1 φχη
2 ifpbi23d.2 φθζ
3 biidd φψψ
4 3 1 2 ifpbi123d φif-ψχθif-ψηζ