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Metamath Proof Explorer

Theorem alimd

Description: Deduction form of Theorem 19.20 of Margaris p. 90, see alim . See alimdh , alimdv for variants requiring fewer axioms. (Contributed by Mario Carneiro, 24-Sep-2016)

	Ref	Expression
Hypotheses	alimd.1	$⊢ Ⅎ x φ$
	alimd.2	$⊢ φ \to (ψ \to χ)$
Assertion	alimd	$⊢ φ \to (\forall x ψ \to \forall x χ)$

Proof

Step	Hyp	Ref	Expression
1		alimd.1	$⊢ Ⅎ x φ$
2		alimd.2	$⊢ φ \to (ψ \to χ)$
3	1	nf5ri	$⊢ φ \to \forall x φ$
4	3 2	alimdh	$⊢ φ \to (\forall x ψ \to \forall x χ)$