Theorem bnj525

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

	Ref	Expression
Hypothesis	bnj525.1	$$⊢A\in \mathrm{V}$$
Assertion	bnj525	$$⊢\underset{\dot{}}{[}A/x\underset{\dot{}}{]}\phi \leftrightarrow \phi$$

Proof

Step	Hyp	Ref	Expression
1		bnj525.1	$$⊢A\in \mathrm{V}$$
2		sbcg	$$⊢A\in \mathrm{V}\to \left(\underset{\dot{}}{[}A/x\underset{\dot{}}{]}\phi \leftrightarrow \phi \right)$$
3	1 2	ax-mp	$$⊢\underset{\dot{}}{[}A/x\underset{\dot{}}{]}\phi \leftrightarrow \phi$$