Theorem axfrege52c

Description: Justification for ax-frege52c . (Contributed by RP, 24-Dec-2019)

	Ref	Expression
Assertion	axfrege52c	$$⊢A=B\to \left(\underset{\dot{}}{[}A/x\underset{\dot{}}{]}\phi \to \underset{\dot{}}{[}B/x\underset{\dot{}}{]}\phi \right)$$

Proof

Step	Hyp	Ref	Expression
1		dfsbcq	$$⊢A=B\to \left(\underset{\dot{}}{[}A/x\underset{\dot{}}{]}\phi \leftrightarrow \underset{\dot{}}{[}B/x\underset{\dot{}}{]}\phi \right)$$
2	1	biimpd	$$⊢A=B\to \left(\underset{\dot{}}{[}A/x\underset{\dot{}}{]}\phi \to \underset{\dot{}}{[}B/x\underset{\dot{}}{]}\phi \right)$$