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Metamath Proof Explorer

Theorem alrimdv

Description: Deduction form of Theorem 19.21 of Margaris p. 90. See 19.21 and 19.21v . (Contributed by NM, 10-Feb-1997)

		Ref	Expression
	Hypothesis	alrimdv.1	$⊢ φ \to (ψ \to χ)$
	Assertion	alrimdv	$⊢ φ \to (ψ \to \forall x χ)$

Step	Hyp	Ref	Expression
1		alrimdv.1	$⊢ φ \to (ψ \to χ)$
2		ax-5	$⊢ φ \to \forall x φ$
3		ax-5	$⊢ ψ \to \forall x ψ$
4	2 3 1	alrimdh	$⊢ φ \to (ψ \to \forall x χ)$