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Theorem 19.2 1723
Description: Theorem 19.2 of [Margaris] p. 89. Note: This proof is very different from Margaris' because we only have Tarski's FOL axiom schemes available at this point. See the later 19.2g 1817 for a more conventional proof of a more general result, which uses additional axioms. (Contributed by NM, 2-Aug-2017.) Remove dependency on ax-7 1739. (Revised by Wolf Lammen, 4-Dec-2017.)
Assertion
Ref Expression
19.2  |-  ( A. x ph  ->  E. x ph )

Proof of Theorem 19.2
StepHypRef Expression
1 id 22 . . 3  |-  ( ph  ->  ph )
21exiftru 1722 . 2  |-  E. x
( ph  ->  ph )
3219.35i 1666 1  |-  ( A. x ph  ->  E. x ph )
Colors of variables: wff setvar class
Syntax hints:    -> wi 4   A.wal 1377   E.wex 1596
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1601  ax-4 1612  ax-6 1719
This theorem depends on definitions:  df-bi 185  df-ex 1597
This theorem is referenced by:  19.8w  1724  19.39  1725  19.24  1726  19.34  1727  eusv2i  4644  extt  29462  pm10.251  30859  ax6e2eq  32419  ax6e2eqVD  32796  bj-19.8w  33325  bj-spnfw  33326
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