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Theorem ax4sp1 1423
Description: A special case of ax-4 1397 without using ax-4 1397 or ax-17 1416. (Contributed by NM, 13-Jan-2011.)
Assertion
Ref Expression
ax4sp1 (y ¬ x = x → ¬ x = x)

Proof of Theorem ax4sp1
StepHypRef Expression
1 equidqe 1422 . 2 ¬ y ¬ x = x
21pm2.21i 574 1 (y ¬ x = x → ¬ x = x)
Colors of variables: wff set class
Syntax hints:  ¬ wn 3  wi 4  wal 1240
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 99  ax-ia2 100  ax-ia3 101  ax-in1 544  ax-in2 545  ax-5 1333  ax-gen 1335  ax-ie2 1380  ax-8 1392  ax-i9 1420
This theorem depends on definitions:  df-bi 110  df-tru 1245  df-fal 1248
This theorem is referenced by: (None)
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