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Theorem 19.28 1500
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 1415 . 2  |-  ( A. x ( ph  /\  ps )  <->  ( A. x ph  /\  A. x ps ) )
2 19.28.1 . . . 4  |-  F/ x ph
3219.3 1491 . . 3  |-  ( A. x ph  <->  ph )
43anbi1i 446 . 2  |-  ( ( A. x ph  /\  A. x ps )  <->  ( ph  /\ 
A. x ps )
)
51, 4bitri 182 1  |-  ( A. x ( ph  /\  ps )  <->  ( ph  /\  A. x ps ) )
Colors of variables: wff set class
Syntax hints:    /\ wa 102    <-> wb 103   A.wal 1287   F/wnf 1394
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 104  ax-ia2 105  ax-ia3 106  ax-5 1381  ax-gen 1383  ax-4 1445
This theorem depends on definitions:  df-bi 115  df-nf 1395
This theorem is referenced by:  aaan  1524
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