Theorem bnj1464

Description: Conversion of implicit substitution to explicit class substitution. (Contributed by Jonathan Ben-Naim, 3-Jun-2011) (New usage is discouraged.)

	Ref	Expression
Hypotheses	bnj1464.1	$$⊢\psi \to \forall x\psi$$
	bnj1464.2	$$⊢x=A\to \left(\phi \leftrightarrow \psi \right)$$
Assertion	bnj1464	$$⊢A\in V\to \left(\underset{\dot{}}{[}A/x\underset{\dot{}}{]}\phi \leftrightarrow \psi \right)$$

Proof

Step	Hyp	Ref	Expression
1		bnj1464.1	$$⊢\psi \to \forall x\psi$$
2		bnj1464.2	$$⊢x=A\to \left(\phi \leftrightarrow \psi \right)$$
3	1	nf5i	$$⊢Ⅎx\psi$$
4	3 2	sbciegf	$$⊢A\in V\to \left(\underset{\dot{}}{[}A/x\underset{\dot{}}{]}\phi \leftrightarrow \psi \right)$$