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Theorem 19.36v 1828
Description: Version of 19.36 2063 with a dv condition instead of a non-freeness hypothesis. (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 1748 . 2  |-  ( E. x ( ph  ->  ps )  <->  ( A. x ph  ->  E. x ps )
)
2 19.9v 1820 . . 3  |-  ( E. x ps  <->  ps )
32imbi2i 319 . 2  |-  ( ( A. x ph  ->  E. x ps )  <->  ( A. x ph  ->  ps )
)
41, 3bitri 257 1  |-  ( E. x ( ph  ->  ps )  <->  ( A. x ph  ->  ps ) )
Colors of variables: wff setvar class
Syntax hints:    -> wi 4    <-> wb 189   A.wal 1450   E.wex 1671
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
This theorem depends on definitions:  df-bi 190  df-ex 1672
This theorem is referenced by:  19.36iv  1829  19.12vvv  1831  19.12vv  2091  axc9lem2  2146  axc9lem2OLD  2147  axext2  2452  vtocl2  3088  vtocl3  3089  bnj1090  29860  bj-spcimdv  31561  19.36vv  36802
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