MPE Home Metamath Proof Explorer < Previous   Next >
Nearby theorems
Mirrors  >  Home  >  MPE Home  >  Th. List  >  19.17 Structured version   Unicode version

Theorem 19.17 2018
Description: Theorem 19.17 of [Margaris] p. 90. (Contributed by NM, 12-Mar-1993.)
Hypothesis
Ref Expression
19.17.1  |-  F/ x ps
Assertion
Ref Expression
19.17  |-  ( A. x ( ph  <->  ps )  ->  ( A. x ph  <->  ps ) )

Proof of Theorem 19.17
StepHypRef Expression
1 albi 1684 . 2  |-  ( A. x ( ph  <->  ps )  ->  ( A. x ph  <->  A. x ps ) )
2 19.17.1 . . 3  |-  F/ x ps
3219.3 1943 . 2  |-  ( A. x ps  <->  ps )
41, 3syl6bb 264 1  |-  ( A. x ( ph  <->  ps )  ->  ( A. x ph  <->  ps ) )
Colors of variables: wff setvar class
Syntax hints:    -> wi 4    <-> wb 187   A.wal 1435   F/wnf 1661
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1663  ax-4 1676  ax-5 1752  ax-6 1798  ax-7 1843  ax-12 1909
This theorem depends on definitions:  df-bi 188  df-ex 1658  df-nf 1662
This theorem is referenced by: (None)
  Copyright terms: Public domain W3C validator