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Metamath Proof Explorer

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	$⊢ ψ \to \forall x ψ$
	bnj1464.2	$⊢ x = A \to (φ \leftrightarrow ψ)$
Assertion	bnj1464	$⊢ A \in V \to (\underset{˙}{[} A / x \underset{˙}{]} φ \leftrightarrow ψ)$

Proof

Step	Hyp	Ref	Expression
1		bnj1464.1	$⊢ ψ \to \forall x ψ$
2		bnj1464.2	$⊢ x = A \to (φ \leftrightarrow ψ)$
3	1	nf5i	$⊢ Ⅎ x ψ$
4	3 2	sbciegf	$⊢ A \in V \to (\underset{˙}{[} A / x \underset{˙}{]} φ \leftrightarrow ψ)$