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Theorem 19.16 2057
Description: Theorem 19.16 of [Margaris] p. 90. (Contributed by NM, 12-Mar-1993.)
Hypothesis
Ref Expression
19.16.1  |-  F/ x ph
Assertion
Ref Expression
19.16  |-  ( A. x ( ph  <->  ps )  ->  ( ph  <->  A. x ps ) )

Proof of Theorem 19.16
StepHypRef Expression
1 19.16.1 . . 3  |-  F/ x ph
2119.3 1986 . 2  |-  ( A. x ph  <->  ph )
3 albi 1698 . 2  |-  ( A. x ( ph  <->  ps )  ->  ( A. x ph  <->  A. x ps ) )
42, 3syl5bbr 267 1  |-  ( A. x ( ph  <->  ps )  ->  ( ph  <->  A. x ps ) )
Colors of variables: wff setvar class
Syntax hints:    -> wi 4    <-> wb 189   A.wal 1450   F/wnf 1675
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1677  ax-4 1690  ax-5 1766  ax-6 1813  ax-7 1859  ax-12 1950
This theorem depends on definitions:  df-bi 190  df-ex 1672  df-nf 1676
This theorem is referenced by: (None)
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