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Metamath Proof Explorer

Theorem ralrid

Description: Sufficient condition for the restricted universal quantifier. Deduction form. (Contributed by Jonathan Ben-Naim, 3-Jun-2011)

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

Step	Hyp	Ref	Expression
1		ralrid.1	$⊢ φ \to \forall x (x \in A \to ψ)$
2		df-ral	$⊢ \forall x \in A ψ \leftrightarrow \forall x (x \in A \to ψ)$
3	1 2	sylibr	$⊢ φ \to \forall x \in A ψ$