Theorem axfrege52a

Description: Justification for ax-frege52a . (Contributed by RP, 17-Apr-2020)

	Ref	Expression
Assertion	axfrege52a	$$⊢\left(\phi \leftrightarrow \psi \right)\to \left(if-\left(\phi ,\theta ,\chi \right)\to if-\left(\psi ,\theta ,\chi \right)\right)$$

Proof

Step	Hyp	Ref	Expression
1		ifpbi1	$$⊢\left(\phi \leftrightarrow \psi \right)\to \left(if-\left(\phi ,\theta ,\chi \right)\leftrightarrow if-\left(\psi ,\theta ,\chi \right)\right)$$
2	1	biimpd	$$⊢\left(\phi \leftrightarrow \psi \right)\to \left(if-\left(\phi ,\theta ,\chi \right)\to if-\left(\psi ,\theta ,\chi \right)\right)$$