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Metamath Proof Explorer

Theorem rspsbca

Description: Restricted quantifier version of Axiom 4 of Mendelson p. 69. (Contributed by NM, 14-Dec-2005)

		Ref	Expression
	Assertion	rspsbca	$⊢ (A \in B \land \forall x \in B φ) \to \underset{˙}{[} A / x \underset{˙}{]} φ$

Step	Hyp	Ref	Expression
1		rspsbc	$⊢ A \in B \to (\forall x \in B φ \to \underset{˙}{[} A / x \underset{˙}{]} φ)$
2	1	imp	$⊢ (A \in B \land \forall x \in B φ) \to \underset{˙}{[} A / x \underset{˙}{]} φ$