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Theorem 19.9h 1991
Description: A wff may be existentially quantified with a variable not free in it. Theorem 19.9 of [Margaris] p. 89. (Contributed by FL, 24-Mar-2007.) (Proof shortened by Wolf Lammen, 5-Jan-2018.) (Proof shortened by Wolf Lammen, 14-Jul-2020.)
Hypothesis
Ref Expression
19.9h.1  |-  ( ph  ->  A. x ph )
Assertion
Ref Expression
19.9h  |-  ( E. x ph  <->  ph )

Proof of Theorem 19.9h
StepHypRef Expression
1 19.9h.1 . . 3  |-  ( ph  ->  A. x ph )
21nfi 1682 . 2  |-  F/ x ph
3219.9 1990 1  |-  ( E. x ph  <->  ph )
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  ax-7 1859  ax-10 1932  ax-12 1950
This theorem depends on definitions:  df-bi 190  df-ex 1672  df-nf 1676
This theorem is referenced by:  19.9OLD  1995  cbv3hvOLD  2081  cbv3hvOLDOLD  2082  bnj1131  29671  bnj1397  29718
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