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Mirrors > Home > ILE Home > Th. List > efrirr | Unicode version |
Description: Irreflexivity of the epsilon relation: a class founded by epsilon is not a member of itself. (Contributed by NM, 18-Apr-1994.) (Revised by Mario Carneiro, 22-Jun-2015.) |
Ref | Expression |
---|---|
efrirr |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | frirrg 4242 | . . . 4 | |
2 | 1 | 3anidm23 1260 | . . 3 |
3 | epelg 4182 | . . . 4 | |
4 | 3 | adantl 275 | . . 3 |
5 | 2, 4 | mtbid 646 | . 2 |
6 | 5 | pm2.01da 610 | 1 |
Colors of variables: wff set class |
Syntax hints: wn 3 wi 4 wa 103 wb 104 wcel 1465 class class class wbr 3899 cep 4179 wfr 4220 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-ia1 105 ax-ia2 106 ax-ia3 107 ax-in1 588 ax-in2 589 ax-io 683 ax-5 1408 ax-7 1409 ax-gen 1410 ax-ie1 1454 ax-ie2 1455 ax-8 1467 ax-10 1468 ax-11 1469 ax-i12 1470 ax-bndl 1471 ax-4 1472 ax-14 1477 ax-17 1491 ax-i9 1495 ax-ial 1499 ax-i5r 1500 ax-ext 2099 ax-sep 4016 ax-pow 4068 ax-pr 4101 |
This theorem depends on definitions: df-bi 116 df-3an 949 df-tru 1319 df-nf 1422 df-sb 1721 df-eu 1980 df-mo 1981 df-clab 2104 df-cleq 2110 df-clel 2113 df-nfc 2247 df-ne 2286 df-ral 2398 df-v 2662 df-dif 3043 df-un 3045 df-in 3047 df-ss 3054 df-pw 3482 df-sn 3503 df-pr 3504 df-op 3506 df-br 3900 df-opab 3960 df-eprel 4181 df-frfor 4223 df-frind 4224 |
This theorem is referenced by: tz7.2 4246 |
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