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Metamath Proof Explorer

Theorem ala1

Description: Add an antecedent in a universally quantified formula. (Contributed by BJ, 6-Oct-2018)

		Ref	Expression
	Assertion	ala1	$⊢ \forall x φ \to \forall x (ψ \to φ)$

Step	Hyp	Ref	Expression
1		ax-1	$⊢ φ \to (ψ \to φ)$
2	1	alimi	$⊢ \forall x φ \to \forall x (ψ \to φ)$