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

Theorem 19.36v 1919
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 1629 . 2  |-  F/ x ps
2119.36 1892 1  |-  ( E. x ( ph  ->  ps )  <->  ( A. x ph  ->  ps ) )
Colors of variables: wff set class
Syntax hints:    -> wi 4    <-> wb 177   A.wal 1549   E.wex 1550
This theorem is referenced by:  19.12vv  1921  ax12olem2  2006  axext2  2418  vtocl2  3007  vtocl3  3008  19.36vv  27558  bnj1090  29348  19.12vvOLD7  29701
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1555  ax-5 1566  ax-17 1626  ax-9 1666  ax-8 1687  ax-6 1744  ax-11 1761
This theorem depends on definitions:  df-bi 178  df-an 361  df-ex 1551  df-nf 1554
  Copyright terms: Public domain W3C validator