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Theorem 19.9 1762
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.) (Revised by Mario Carneiro, 24-Sep-2016.)
Hypothesis
Ref Expression
19.9.1  |-  F/ x ph
Assertion
Ref Expression
19.9  |-  ( E. x ph  <->  ph )

Proof of Theorem 19.9
StepHypRef Expression
1 19.9.1 . 2  |-  F/ x ph
2 19.9t 1761 . 2  |-  ( F/ x ph  ->  ( E. x ph  <->  ph ) )
31, 2ax-mp 10 1  |-  ( E. x ph  <->  ph )
Colors of variables: wff set class
Syntax hints:    <-> wb 178   E.wex 1537   F/wnf 1539
This theorem is referenced by:  excomim  1764  19.19  1769  19.36  1788  19.44  1796  19.45  1797  exdistrf  1863  19.9v  2010  exists1  2202  dfid3  4203  fsplit  6075  a9e2ndeq  27018  e2ebind  27022  a9e2ndeqVD  27375  e2ebindVD  27378  e2ebindALT  27396  a9e2ndeqALT  27398  bnj1131  27508  bnj1397  27556  bnj1189  27728
This theorem was proved from axioms:  ax-1 7  ax-2 8  ax-3 9  ax-mp 10  ax-5 1533  ax-6 1534  ax-gen 1536  ax-4 1692
This theorem depends on definitions:  df-bi 179  df-ex 1538  df-nf 1540
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