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 ( 𝜑𝜓 )
Assertion sps-o ( ∀ 𝑥 𝜑𝜓 )

Proof

Step Hyp Ref Expression
1 sps-o.1 ( 𝜑𝜓 )
2 ax-c5 ( ∀ 𝑥 𝜑𝜑 )
3 2 1 syl ( ∀ 𝑥 𝜑𝜓 )