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Metamath Proof Explorer

Theorem r19.21be

Description: Inference from Theorem 19.21 of Margaris p. 90. (Restricted quantifier version.) (Contributed by NM, 21-Nov-1994)

		Ref	Expression
	Hypothesis	r19.21be.1	$⊢ φ \to \forall x \in A ψ$
	Assertion	r19.21be	$⊢ \forall x \in A (φ \to ψ)$

Step	Hyp	Ref	Expression
1		r19.21be.1	$⊢ φ \to \forall x \in A ψ$
2	1	r19.21bi	$⊢ (φ \land x \in A) \to ψ$
3	2	expcom	$⊢ x \in A \to (φ \to ψ)$
4	3	rgen	$⊢ \forall x \in A (φ \to ψ)$