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 → 𝜓 )
Assertion	sps-o	⊢ ( ∀ 𝑥 𝜑 → 𝜓 )

Proof

Step	Hyp	Ref	Expression
1		sps-o.1	⊢ ( 𝜑 → 𝜓 )
2		ax-c5	⊢ ( ∀ 𝑥 𝜑 → 𝜑 )
3	2 1	syl	⊢ ( ∀ 𝑥 𝜑 → 𝜓 )