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Theorem ax9dgen 1716
Description: Tarski's system uses the weaker ax9v 1655 instead of the bundled ax-9 1654, so here we show that the degenerate case of ax-9 1654 can be derived. (Contributed by NM, 23-Apr-2017.)
Assertion
Ref Expression
ax9dgen ¬ x ¬ x = x

Proof of Theorem ax9dgen
StepHypRef Expression
1 equid 1676 . 2 x = x
21notnoti 115 . . 3 ¬ ¬ x = x
32spfalw 1672 . 2 (x ¬ x = x → ¬ x = x)
41, 3mt2 170 1 ¬ x ¬ x = x
Colors of variables: wff setvar class
Syntax hints:  ¬ wn 3  wal 1540
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1546  ax-5 1557  ax-17 1616  ax-9 1654  ax-8 1675
This theorem depends on definitions:  df-bi 177  df-an 360  df-ex 1542
This theorem is referenced by: (None)
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