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Theorem 19.23 1915
Description: Theorem 19.23 of [Margaris] p. 90. See 19.23v 1765 for a version requiring fewer axioms. (Contributed by NM, 24-Jan-1993.) (Revised by Mario Carneiro, 24-Sep-2016.)
Hypothesis
Ref Expression
19.23.1  |-  F/ x ps
Assertion
Ref Expression
19.23  |-  ( A. x ( ph  ->  ps )  <->  ( E. x ph  ->  ps ) )

Proof of Theorem 19.23
StepHypRef Expression
1 19.23.1 . 2  |-  F/ x ps
2 19.23t 1914 . 2  |-  ( F/ x ps  ->  ( A. x ( ph  ->  ps )  <->  ( E. x ph  ->  ps ) ) )
31, 2ax-mp 5 1  |-  ( A. x ( ph  ->  ps )  <->  ( E. x ph  ->  ps ) )
Colors of variables: wff setvar class
Syntax hints:    -> wi 4    <-> wb 184   A.wal 1396   E.wex 1617   F/wnf 1621
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1623  ax-4 1636  ax-5 1709  ax-6 1752  ax-7 1795  ax-10 1842  ax-12 1859
This theorem depends on definitions:  df-bi 185  df-ex 1618  df-nf 1622
This theorem is referenced by:  19.23h  1916  exlimi  1917  nf2  1965  19.23vOLD  1987  pm11.53  1988  equsal  2040  2sb6rf  2198  axc11n-16  2270  r19.3rz  3908  ralidm  3921  ssrelf  27681  axc11next  31554  bj-biexal1  34660  bj-biexex  34664  bj-equsalv  34710
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