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Theorem ax4sp1 1533
Description: A special case of ax-4 1510 without using ax-4 1510 or ax-17 1526. (Contributed by NM, 13-Jan-2011.)
Assertion
Ref Expression
ax4sp1 (∀𝑦 ¬ 𝑥 = 𝑥 → ¬ 𝑥 = 𝑥)

Proof of Theorem ax4sp1
StepHypRef Expression
1 equidqe 1532 . 2 ¬ ∀𝑦 ¬ 𝑥 = 𝑥
21pm2.21i 646 1 (∀𝑦 ¬ 𝑥 = 𝑥 → ¬ 𝑥 = 𝑥)
Colors of variables: wff set class
Syntax hints:  ¬ wn 3  wi 4  wal 1351
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 106  ax-ia2 107  ax-ia3 108  ax-in1 614  ax-in2 615  ax-5 1447  ax-gen 1449  ax-ie2 1494  ax-8 1504  ax-i9 1530
This theorem depends on definitions:  df-bi 117  df-tru 1356  df-fal 1359
This theorem is referenced by: (None)
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