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Mirrors > Home > ILE Home > Th. List > ax4sp1 | GIF version |
Description: A special case of ax-4 1510 without using ax-4 1510 or ax-17 1526. (Contributed by NM, 13-Jan-2011.) |
Ref | Expression |
---|---|
ax4sp1 | ⊢ (∀𝑦 ¬ 𝑥 = 𝑥 → ¬ 𝑥 = 𝑥) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | equidqe 1532 | . 2 ⊢ ¬ ∀𝑦 ¬ 𝑥 = 𝑥 | |
2 | 1 | pm2.21i 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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