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Theorem 19.36v 1935
Description: Special case of Theorem 19.36 of [Margaris] p. 90. (Contributed by NM, 18-Aug-1993.) Reduce dependencies on axioms. (Revised by Wolf Lammen, 17-Jan-2020.)
Assertion
Ref Expression
19.36v  |-  ( E. x ( ph  ->  ps )  <->  ( A. x ph  ->  ps ) )
Distinct variable group:    ps, x
Allowed substitution hint:    ph( x)

Proof of Theorem 19.36v
StepHypRef Expression
1 19.35 1664 . 2  |-  ( E. x ( ph  ->  ps )  <->  ( A. x ph  ->  E. x ps )
)
2 19.9v 1728 . . 3  |-  ( E. x ps  <->  ps )
32imbi2i 312 . 2  |-  ( ( A. x ph  ->  E. x ps )  <->  ( A. x ph  ->  ps )
)
41, 3bitri 249 1  |-  ( E. x ( ph  ->  ps )  <->  ( A. x ph  ->  ps ) )
Colors of variables: wff setvar class
Syntax hints:    -> wi 4    <-> wb 184   A.wal 1377   E.wex 1596
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1601  ax-4 1612  ax-5 1680  ax-6 1719
This theorem depends on definitions:  df-bi 185  df-ex 1597
This theorem is referenced by:  19.36aiv  1936  19.12vv  1942  axc9lem2  2013  axext2  2446  vtocl2  3171  vtocl3  3172  19.36vv  31190  bnj1090  33515
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