MPE Home Metamath Proof Explorer < Previous   Next >
Nearby theorems
Mirrors  >  Home  >  MPE Home  >  Th. List  >  19.36v Structured version   Unicode version

Theorem 19.36v 1927
Description: Special case of Theorem 19.36 of [Margaris] p. 90. (Contributed by NM, 18-Aug-1993.)
Assertion
Ref Expression
19.36v  |-  ( E. x ( ph  ->  ps )  <->  ( A. x ph  ->  ps ) )
Distinct variable group:    ps, x
Allowed substitution hint:    ph( x)

Proof of Theorem 19.36v
StepHypRef Expression
1 nfv 1674 . 2  |-  F/ x ps
2119.36 1904 1  |-  ( E. x ( ph  ->  ps )  <->  ( A. x ph  ->  ps ) )
Colors of variables: wff setvar class
Syntax hints:    -> wi 4    <-> wb 184   A.wal 1368   E.wex 1587
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1592  ax-4 1603  ax-5 1671  ax-6 1710  ax-7 1730  ax-10 1777  ax-12 1794
This theorem depends on definitions:  df-bi 185  df-ex 1588  df-nf 1591
This theorem is referenced by:  19.12vv  1929  axc9lem2  2000  axext2  2433  vtocl2  3131  vtocl3  3132  19.36vv  29806  bnj1090  32325
  Copyright terms: Public domain W3C validator