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Theorem 19.28 1843
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 1604 . 2  |-  ( A. x ( ph  /\  ps )  <->  ( A. x ph  /\  A. x ps ) )
2 19.28.1 . . . 4  |-  F/ x ph
3219.3 1792 . . 3  |-  ( A. x ph  <->  ph )
43anbi1i 678 . 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 1550   F/wnf 1554
This theorem is referenced by:  nfan1  1846  exanOLD  1905  aaan  1907  19.28v  1919  aaanOLD7  29772
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1556  ax-5 1567  ax-17 1627  ax-9 1667  ax-8 1688  ax-11 1762
This theorem depends on definitions:  df-bi 179  df-an 362  df-ex 1552  df-nf 1555
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