Metamath Proof Explorer


Theorem spimvw

Description: A weak form of specialization. Lemma 8 of KalishMontague p. 87. Uses only Tarski's FOL axiom schemes. For stronger forms using more axioms, see spimv and spimfv . (Contributed by NM, 9-Apr-2017)

Ref Expression
Hypothesis spimvw.1
|- ( x = y -> ( ph -> ps ) )
Assertion spimvw
|- ( A. x ph -> ps )

Proof

Step Hyp Ref Expression
1 spimvw.1
 |-  ( x = y -> ( ph -> ps ) )
2 ax-5
 |-  ( -. ps -> A. x -. ps )
3 2 1 spimw
 |-  ( A. x ph -> ps )