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Metamath Proof Explorer

Theorem sps

Description: Generalization of antecedent. (Contributed by NM, 5-Jan-1993)

		Ref	Expression
	Hypothesis	sps.1	$⊢ φ \to ψ$
	Assertion	sps	$⊢ \forall x φ \to ψ$

Step	Hyp	Ref	Expression
1		sps.1	$⊢ φ \to ψ$
2		sp	$⊢ \forall x φ \to φ$
3	2 1	syl	$⊢ \forall x φ \to ψ$