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Metamath Proof Explorer

Theorem ralrimiv

Description: Inference from Theorem 19.21 of Margaris p. 90. (Restricted quantifier version.) (Contributed by NM, 22-Nov-1994) Reduce dependencies on axioms. (Revised by Wolf Lammen, 4-Dec-2019)

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

Proof

Step	Hyp	Ref	Expression
1		ralrimiv.1	$⊢ φ \to (x \in A \to ψ)$
2		ax-5	$⊢ φ \to \forall x φ$
3	2 1	hbralrimi	$⊢ φ \to \forall x \in A ψ$