Theorem bnj524

Description: First-order logic and set theory. (Contributed by Jonathan Ben-Naim, 3-Jun-2011) (New usage is discouraged.)

	Ref	Expression
Hypotheses	bnj524.1	$$⊢\phi \leftrightarrow \psi$$
	bnj524.2	$$⊢A\in \mathrm{V}$$
Assertion	bnj524	$$⊢\underset{\dot{}}{[}A/x\underset{\dot{}}{]}\phi \leftrightarrow \underset{\dot{}}{[}A/x\underset{\dot{}}{]}\psi$$

Proof

Step	Hyp	Ref	Expression
1		bnj524.1	$$⊢\phi \leftrightarrow \psi$$
2		bnj524.2	$$⊢A\in \mathrm{V}$$
3	1	sbcbii	$$⊢\underset{\dot{}}{[}A/x\underset{\dot{}}{]}\phi \leftrightarrow \underset{\dot{}}{[}A/x\underset{\dot{}}{]}\psi$$