MPE Home Metamath Proof Explorer < Previous   Next >
Nearby theorems
Mirrors  >  Home  >  MPE Home  >  Th. List  >  spimvw Unicode version

Theorem spimvw 1669
Description: Specialization. Lemma 8 of [KalishMontague] p. 87. Uses only Tarski's FOL axiom schemes. (Contributed by NM, 9-Apr-2017.)
Hypothesis
Ref Expression
spimvw.1  |-  ( x  =  y  ->  ( ph  ->  ps ) )
Assertion
Ref Expression
spimvw  |-  ( A. x ph  ->  ps )
Distinct variable groups:    x, y    ps, x
Allowed substitution hints:    ph( x, y)    ps( y)

Proof of Theorem spimvw
StepHypRef Expression
1 ax-17 1616 . 2  |-  ( -. 
ps  ->  A. x  -.  ps )
2 spimvw.1 . 2  |-  ( x  =  y  ->  ( ph  ->  ps ) )
31, 2spimw 1668 1  |-  ( A. x ph  ->  ps )
Colors of variables: wff set class
Syntax hints:   -. wn 3    -> wi 4   A.wal 1540
This theorem is referenced by:  cbvalivw  1674  spw  1694  alcomiw  1704
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1546  ax-5 1557  ax-17 1616  ax-9 1654
This theorem depends on definitions:  df-bi 177  df-an 360  df-ex 1542
  Copyright terms: Public domain W3C validator