MPE Home Metamath Proof Explorer < Previous   Next >
Nearby theorems
Mirrors  >  Home  >  MPE Home  >  Th. List  >  a4imv Unicode version

Theorem a4imv 1922
Description: A version of a4im 1867 with a distinct variable requirement instead of a bound variable hypothesis. (Contributed by NM, 5-Aug-1993.)
Hypothesis
Ref Expression
a4imv.1  |-  ( x  =  y  ->  ( ph  ->  ps ) )
Assertion
Ref Expression
a4imv  |-  ( A. x ph  ->  ps )
Distinct variable group:    ps, x
Allowed substitution hints:    ph( x, y)    ps( y)

Proof of Theorem a4imv
StepHypRef Expression
1 nfv 1629 . 2  |-  F/ x ps
2 a4imv.1 . 2  |-  ( x  =  y  ->  ( ph  ->  ps ) )
31, 2a4im 1867 1  |-  ( A. x ph  ->  ps )
Colors of variables: wff set class
Syntax hints:    -> wi 6   A.wal 1532
This theorem is referenced by:  aev  1923  aev-o  1924  ax16i  1994  a4v  1996  reu6  2893  el  4086  ax10ext  26772
This theorem was proved from axioms:  ax-1 7  ax-2 8  ax-3 9  ax-mp 10  ax-5 1533  ax-6 1534  ax-gen 1536  ax-17 1628  ax-9 1684  ax-4 1692
This theorem depends on definitions:  df-bi 179  df-an 362  df-tru 1315  df-nf 1540
  Copyright terms: Public domain W3C validator