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Theorem ax9dgen 1732
Description: Tarski's system uses the weaker ax9v 1668 instead of the bundled ax-9 1667, so here we show that the degenerate case of ax-9 1667 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 1689 . 2  |-  x  =  x
21notnoti 118 . . 3  |-  -.  -.  x  =  x
32spfalw 1685 . 2  |-  ( A. x  -.  x  =  x  ->  -.  x  =  x )
41, 3mt2 173 1  |-  -.  A. x  -.  x  =  x
Colors of variables: wff set class
Syntax hints:   -. wn 3   A.wal 1550
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1556  ax-5 1567  ax-17 1627  ax-9 1667  ax-8 1688
This theorem depends on definitions:  df-bi 179  df-an 362  df-ex 1552
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