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Theorem ax6dgen 1829
Description: Tarski's system uses the weaker ax6v 1753 instead of the bundled ax-6 1752, so here we show that the degenerate case of ax-6 1752 can be derived. (Contributed by NM, 23-Apr-2017.)
Assertion
Ref Expression
ax6dgen  |-  -.  A. x  -.  x  =  x

Proof of Theorem ax6dgen
StepHypRef Expression
1 equid 1796 . 2  |-  x  =  x
21notnoti 123 . . 3  |-  -.  -.  x  =  x
32spfalw 1791 . 2  |-  ( A. x  -.  x  =  x  ->  -.  x  =  x )
41, 3mt2 179 1  |-  -.  A. x  -.  x  =  x
Colors of variables: wff setvar class
Syntax hints:   -. wn 3   A.wal 1396
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1623  ax-4 1636  ax-5 1709  ax-6 1752  ax-7 1795
This theorem depends on definitions:  df-bi 185  df-ex 1618
This theorem is referenced by: (None)
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