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Theorem ax4sp1 1357
Description: A special case of ax-4 1333 without using ax-4 1333 or ax-17 1349. (Contributed by NM, 13-Jan-2011.)
Assertion
Ref Expression
ax4sp1 (y ¬ x = x → ¬ x = x)

Proof of Theorem ax4sp1
StepHypRef Expression
1 equidqe 1355 . 2 ¬ y ¬ x = x
21pm2.21i 553 1 (y ¬ x = x → ¬ x = x)
Colors of variables: wff set class
Syntax hints:  ¬ wn 3  wi 4  wal 1266
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 97  ax-ia2 98  ax-ia3 99  ax-in1 526  ax-in2 527  ax-5 1267  ax-gen 1269  ax-ie2 1315  ax-8 1328  ax-i9 1353
This theorem depends on definitions:  df-bi 108  df-tru 1201  df-fal 1202
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