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Theorem ax9dgen 1702
Description: Tarski's system uses the weaker ax9v 1645 instead of the bundled ax-9 1644, so here we show that the degenerate case of ax-9 1644 can be derived. (Contributed by NM, 23-Apr-2017.)
Assertion
Ref Expression
ax9dgen  |-  -.  A. x  -.  x  =  x

Proof of Theorem ax9dgen
StepHypRef Expression
1 equid 1662 . 2  |-  x  =  x
21notnoti 115 . . 3  |-  -.  -.  x  =  x
32spfalw 1685 . 2  |-  ( A. x  -.  x  =  x  ->  -.  x  =  x )
41, 3mt2 170 1  |-  -.  A. x  -.  x  =  x
Colors of variables: wff set class
Syntax hints:   -. wn 3   A.wal 1530
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1536  ax-5 1547  ax-17 1606  ax-9 1644  ax-8 1661
This theorem depends on definitions:  df-bi 177  df-an 360  df-tru 1310  df-fal 1311  df-ex 1532
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