MPE Home Metamath Proof Explorer < Previous   Next >
Nearby theorems
Mirrors  >  Home  >  MPE Home  >  Th. List  >  19.27 Structured version   Unicode version

Theorem 19.27 1841
Description: Theorem 19.27 of [Margaris] p. 90. (Contributed by NM, 5-Aug-1993.)
Hypothesis
Ref Expression
19.27.1  |-  F/ x ps
Assertion
Ref Expression
19.27  |-  ( A. x ( ph  /\  ps )  <->  ( A. x ph  /\  ps ) )

Proof of Theorem 19.27
StepHypRef Expression
1 19.26 1603 . 2  |-  ( A. x ( ph  /\  ps )  <->  ( A. x ph  /\  A. x ps ) )
2 19.27.1 . . . 4  |-  F/ x ps
3219.3 1791 . . 3  |-  ( A. x ps  <->  ps )
43anbi2i 676 . 2  |-  ( ( A. x ph  /\  A. x ps )  <->  ( A. x ph  /\  ps )
)
51, 4bitri 241 1  |-  ( A. x ( ph  /\  ps )  <->  ( A. x ph  /\  ps ) )
Colors of variables: wff set class
Syntax hints:    <-> wb 177    /\ wa 359   A.wal 1549   F/wnf 1553
This theorem is referenced by:  aaan  1906  19.27v  1917  aaanOLD7  29698
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-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