This is an inofficial mirror of http://metamath.tirix.org for personal testing of a visualizer extension only.

Metamath Proof Explorer

Theorem spsd

Description: Deduction generalizing antecedent. (Contributed by NM, 17-Aug-1994)

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

Step	Hyp	Ref	Expression
1		spsd.1	$⊢ φ \to (ψ \to χ)$
2		sp	$⊢ \forall x ψ \to ψ$
3	2 1	syl5	$⊢ φ \to (\forall x ψ \to χ)$