Theorem sbcieg

Description: Conversion of implicit substitution to explicit class substitution. (Contributed by NM, 10-Nov-2005)

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

Proof

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