![]() |
Intuitionistic Logic Explorer |
< Previous
Next >
Nearby theorems |
|
Mirrors > Home > ILE Home > Th. List > 1ne0 | GIF version |
Description: 1 ≠ 0. See aso 1ap0 8578. (Contributed by Jim Kingdon, 9-Mar-2020.) |
Ref | Expression |
---|---|
1ne0 | ⊢ 1 ≠ 0 |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | 0ne1 9017 | . 2 ⊢ 0 ≠ 1 | |
2 | 1 | necomi 2445 | 1 ⊢ 1 ≠ 0 |
Colors of variables: wff set class |
Syntax hints: ≠ wne 2360 0cc0 7842 1c1 7843 |
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 615 ax-in2 616 ax-io 710 ax-5 1458 ax-7 1459 ax-gen 1460 ax-ie1 1504 ax-ie2 1505 ax-8 1515 ax-10 1516 ax-11 1517 ax-i12 1518 ax-bndl 1520 ax-4 1521 ax-17 1537 ax-i9 1541 ax-ial 1545 ax-i5r 1546 ax-13 2162 ax-14 2163 ax-ext 2171 ax-sep 4136 ax-pow 4192 ax-pr 4227 ax-un 4451 ax-setind 4554 ax-cnex 7933 ax-resscn 7934 ax-1re 7936 ax-addrcl 7939 ax-0lt1 7948 ax-rnegex 7951 ax-pre-ltirr 7954 |
This theorem depends on definitions: df-bi 117 df-3an 982 df-tru 1367 df-fal 1370 df-nf 1472 df-sb 1774 df-eu 2041 df-mo 2042 df-clab 2176 df-cleq 2182 df-clel 2185 df-nfc 2321 df-ne 2361 df-nel 2456 df-ral 2473 df-rex 2474 df-rab 2477 df-v 2754 df-dif 3146 df-un 3148 df-in 3150 df-ss 3157 df-pw 3592 df-sn 3613 df-pr 3614 df-op 3616 df-uni 3825 df-br 4019 df-opab 4080 df-xp 4650 df-pnf 8025 df-mnf 8026 df-ltxr 8028 |
This theorem is referenced by: neg1ne0 9057 efne0 11721 mod2eq1n2dvds 11919 m1exp1 11941 gcd1 12023 rpdvds 12134 m1dvdsndvds 12283 pcpre1 12327 pc1 12340 pcrec 12343 pcid 12359 zringnzr 13918 lgsne0 14917 1lgs 14922 2sqlem7 14946 2sqlem8a 14947 2sqlem8 14948 trirec0xor 15272 dceqnconst 15287 dcapnconst 15288 |
Copyright terms: Public domain | W3C validator |