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Mirrors > Home > ILE Home > Th. List > 1ne0 | GIF version |
Description: 1 ≠ 0. See aso 1ap0 8164. (Contributed by Jim Kingdon, 9-Mar-2020.) |
Ref | Expression |
---|---|
1ne0 | ⊢ 1 ≠ 0 |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | 0ne1 8587 | . 2 ⊢ 0 ≠ 1 | |
2 | 1 | necomi 2347 | 1 ⊢ 1 ≠ 0 |
Colors of variables: wff set class |
Syntax hints: ≠ wne 2262 0cc0 7447 1c1 7448 |
This theorem was proved from axioms: ax-1 5 ax-2 6 ax-mp 7 ax-ia1 105 ax-ia2 106 ax-ia3 107 ax-in1 582 ax-in2 583 ax-io 668 ax-5 1388 ax-7 1389 ax-gen 1390 ax-ie1 1434 ax-ie2 1435 ax-8 1447 ax-10 1448 ax-11 1449 ax-i12 1450 ax-bndl 1451 ax-4 1452 ax-13 1456 ax-14 1457 ax-17 1471 ax-i9 1475 ax-ial 1479 ax-i5r 1480 ax-ext 2077 ax-sep 3978 ax-pow 4030 ax-pr 4060 ax-un 4284 ax-setind 4381 ax-cnex 7533 ax-resscn 7534 ax-1re 7536 ax-addrcl 7539 ax-0lt1 7548 ax-rnegex 7551 ax-pre-ltirr 7554 |
This theorem depends on definitions: df-bi 116 df-3an 929 df-tru 1299 df-fal 1302 df-nf 1402 df-sb 1700 df-eu 1958 df-mo 1959 df-clab 2082 df-cleq 2088 df-clel 2091 df-nfc 2224 df-ne 2263 df-nel 2358 df-ral 2375 df-rex 2376 df-rab 2379 df-v 2635 df-dif 3015 df-un 3017 df-in 3019 df-ss 3026 df-pw 3451 df-sn 3472 df-pr 3473 df-op 3475 df-uni 3676 df-br 3868 df-opab 3922 df-xp 4473 df-pnf 7621 df-mnf 7622 df-ltxr 7624 |
This theorem is referenced by: neg1ne0 8627 efne0 11117 mod2eq1n2dvds 11306 m1exp1 11328 gcd1 11405 rpdvds 11508 |
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