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Theorem 19.28 1952
Description: Theorem 19.28 of [Margaris] p. 90. See 19.28v 1791 for a version requiring fewer axioms. (Contributed by NM, 1-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 1701 . 2  |-  ( A. x ( ph  /\  ps )  <->  ( A. x ph  /\  A. x ps ) )
2 19.28.1 . . . 4  |-  F/ x ph
3219.3 1912 . . 3  |-  ( A. x ph  <->  ph )
43anbi1i 693 . 2  |-  ( ( A. x ph  /\  A. x ps )  <->  ( ph  /\ 
A. x ps )
)
51, 4bitri 249 1  |-  ( A. x ( ph  /\  ps )  <->  ( ph  /\  A. x ps ) )
Colors of variables: wff setvar class
Syntax hints:    <-> wb 184    /\ wa 367   A.wal 1403   F/wnf 1637
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1639  ax-4 1652  ax-5 1725  ax-6 1771  ax-7 1814  ax-12 1878
This theorem depends on definitions:  df-bi 185  df-an 369  df-ex 1634  df-nf 1638
This theorem is referenced by:  nfan1  1955  aaan  2003  wl-ax11-lem7  31403
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