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Theorem 19.36 1874
Description: Theorem 19.36 of [Margaris] p. 90. (Contributed by NM, 5-Aug-1993.)
Hypothesis
Ref Expression
19.36.1  |-  F/ x ps
Assertion
Ref Expression
19.36  |-  ( E. x ( ph  ->  ps )  <->  ( A. x ph  ->  ps ) )

Proof of Theorem 19.36
StepHypRef Expression
1 19.35 1600 . 2  |-  ( E. x ( ph  ->  ps )  <->  ( A. x ph  ->  E. x ps )
)
2 19.36.1 . . . 4  |-  F/ x ps
3219.9 1784 . . 3  |-  ( E. x ps  <->  ps )
43imbi2i 303 . 2  |-  ( ( A. x ph  ->  E. x ps )  <->  ( A. x ph  ->  ps )
)
51, 4bitri 240 1  |-  ( E. x ( ph  ->  ps )  <->  ( A. x ph  ->  ps ) )
Colors of variables: wff set class
Syntax hints:    -> wi 4    <-> wb 176   A.wal 1540   E.wex 1541   F/wnf 1544
This theorem is referenced by:  19.36i  1875  19.36v  1901  19.12vv  1903  spcimgft  2935  19.12b  24716  19.12vvOLD7  29085
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1546  ax-5 1557  ax-17 1616  ax-9 1654  ax-8 1675  ax-6 1729  ax-11 1746
This theorem depends on definitions:  df-bi 177  df-an 360  df-ex 1542  df-nf 1545
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