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Theorem 19.27 1525
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 1442 . 2  |-  ( A. x ( ph  /\  ps )  <->  ( A. x ph  /\  A. x ps ) )
2 19.27.1 . . . 4  |-  F/ x ps
3219.3 1518 . . 3  |-  ( A. x ps  <->  ps )
43anbi2i 452 . 2  |-  ( ( A. x ph  /\  A. x ps )  <->  ( A. x ph  /\  ps )
)
51, 4bitri 183 1  |-  ( A. x ( ph  /\  ps )  <->  ( A. x ph  /\  ps ) )
Colors of variables: wff set class
Syntax hints:    /\ wa 103    <-> wb 104   A.wal 1314   F/wnf 1421
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 105  ax-ia2 106  ax-ia3 107  ax-5 1408  ax-gen 1410  ax-4 1472
This theorem depends on definitions:  df-bi 116  df-nf 1422
This theorem is referenced by:  aaan  1551
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