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Theorem 19.36iv 1829
Description: Inference associated with 19.36v 1828. Version of 19.36i 2064 with a dv condition. (Contributed by NM, 5-Aug-1993.) Reduce dependencies on axioms. (Revised by Wolf Lammen, 17-Jan-2020.)
Hypothesis
Ref Expression
19.36iv.1  |-  E. x
( ph  ->  ps )
Assertion
Ref Expression
19.36iv  |-  ( A. x ph  ->  ps )
Distinct variable group:    ps, x
Allowed substitution hint:    ph( x)

Proof of Theorem 19.36iv
StepHypRef Expression
1 19.36iv.1 . 2  |-  E. x
( ph  ->  ps )
2 19.36v 1828 . 2  |-  ( E. x ( ph  ->  ps )  <->  ( A. x ph  ->  ps ) )
31, 2mpbi 213 1  |-  ( A. x ph  ->  ps )
Colors of variables: wff setvar class
Syntax hints:    -> wi 4   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:  spimv  2114  vtocl  3086  vtocl2  3088  vtocl3  3089  zfcndext  9056  bj-spimvv  31388
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