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Theorem 19.27 1786
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 1592 . 2  |-  ( A. x ( ph  /\  ps )  <->  ( A. x ph  /\  A. x ps ) )
2 19.27.1 . . . 4  |-  F/ x ps
3219.3 1760 . . 3  |-  ( A. x ps  <->  ps )
43anbi2i 678 . 2  |-  ( ( A. x ph  /\  A. x ps )  <->  ( A. x ph  /\  ps )
)
51, 4bitri 242 1  |-  ( A. x ( ph  /\  ps )  <->  ( A. x ph  /\  ps ) )
Colors of variables: wff set class
Syntax hints:    <-> wb 178    /\ wa 360   A.wal 1532   F/wnf 1539
This theorem is referenced by:  aaan  1811  19.27v  2027
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
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