Theorem spsd

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

	Ref	Expression
Hypothesis	spsd.1	$$⊢\phi \to \left(\psi \to \chi \right)$$
Assertion	spsd	$$⊢\phi \to \left(\forall x\psi \to \chi \right)$$

Proof

Step	Hyp	Ref	Expression
1		spsd.1	$$⊢\phi \to \left(\psi \to \chi \right)$$
2		sp	$$⊢\forall x\psi \to \psi$$
3	2 1	syl5	$$⊢\phi \to \left(\forall x\psi \to \chi \right)$$