MPE Home Metamath Proof Explorer < Previous   Next >
Nearby theorems
Mirrors  >  Home  >  MPE Home  >  Th. List  >  19.28 Unicode version

Theorem 19.28 1787
Description: Theorem 19.28 of [Margaris] p. 90. (Contributed by NM, 5-Aug-1993.)
Hypothesis
Ref Expression
19.28.1  |-  F/ x ph
Assertion
Ref Expression
19.28  |-  ( A. x ( ph  /\  ps )  <->  ( ph  /\  A. x ps ) )

Proof of Theorem 19.28
StepHypRef Expression
1 19.26 1592 . 2  |-  ( A. x ( ph  /\  ps )  <->  ( A. x ph  /\  A. x ps ) )
2 19.28.1 . . . 4  |-  F/ x ph
3219.3 1760 . . 3  |-  ( A. x ph  <->  ph )
43anbi1i 679 . 2  |-  ( ( A. x ph  /\  A. x ps )  <->  ( ph  /\ 
A. x ps )
)
51, 4bitri 242 1  |-  ( A. x ( ph  /\  ps )  <->  ( ph  /\  A. x ps ) )
Colors of variables: wff set class
Syntax hints:    <-> wb 178    /\ wa 360   A.wal 1532   F/wnf 1539
This theorem is referenced by:  nfan1  1806  exan  1807  aaan  1811  19.28v  2029
This theorem was proved from axioms:  ax-1 7  ax-2 8  ax-3 9  ax-mp 10  ax-5 1533  ax-gen 1536  ax-4 1692
This theorem depends on definitions:  df-bi 179  df-an 362  df-nf 1540
  Copyright terms: Public domain W3C validator