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Metamath Proof Explorer

Theorem sps-o

Description: Generalization of antecedent. (Contributed by NM, 5-Jan-1993) (Proof modification is discouraged.) (New usage is discouraged.)

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

Step	Hyp	Ref	Expression
1		sps-o.1	$⊢ φ \to ψ$
2		ax-c5	$⊢ \forall x φ \to φ$
3	2 1	syl	$⊢ \forall x φ \to ψ$