Metamath Proof Explorer


Theorem spsv

Description: Generalization of antecedent. A trivial weak version of sps avoiding ax-12 . (Contributed by SN, 13-Nov-2025) (Proof shortened by WL, 19-Nov-2025)

Ref Expression
Hypothesis spsv.1
|- ( ph -> ps )
Assertion spsv
|- ( A. x ph -> ps )

Proof

Step Hyp Ref Expression
1 spsv.1
 |-  ( ph -> ps )
2 1 a1i
 |-  ( x = y -> ( ph -> ps ) )
3 2 spimvw
 |-  ( A. x ph -> ps )