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Theorem 19.2 1671
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 1780 for a more conventional proof. (Contributed by NM, 2-Aug-2017.)
Assertion
Ref Expression
19.2  |-  ( A. x ph  ->  E. x ph )

Proof of Theorem 19.2
StepHypRef Expression
1 equid 1644 . . 3  |-  x  =  x
21notnoti 115 . . . 4  |-  -.  -.  x  =  x
32spfalw 1670 . . 3  |-  ( A. x  -.  x  =  x  ->  -.  x  =  x )
41, 3mt2 170 . 2  |-  -.  A. x  -.  x  =  x
5 idd 21 . . 3  |-  ( x  =  x  ->  ( ph  ->  ph ) )
65speimfw 1626 . 2  |-  ( -. 
A. x  -.  x  =  x  ->  ( A. x ph  ->  E. x ph ) )
74, 6ax-mp 8 1  |-  ( A. x ph  ->  E. x ph )
Colors of variables: wff set class
Syntax hints:   -. wn 3    -> wi 4   A.wal 1527   E.wex 1528
This theorem is referenced by:  19.39  1672  19.24  1673  19.34  1674  eusv2i  4531  extt  24843  pm10.251  27555  a9e2eq  28323  a9e2eqVD  28683
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1533  ax-5 1544  ax-17 1603  ax-9 1635  ax-8 1643
This theorem depends on definitions:  df-bi 177  df-an 360  df-tru 1310  df-fal 1311  df-ex 1529
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