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Mirrors > Home > ILE Home > Th. List > dfnul2 | Unicode version |
Description: Alternate definition of the empty set. Definition 5.14 of [TakeutiZaring] p. 20. (Contributed by NM, 26-Dec-1996.) |
Ref | Expression |
---|---|
dfnul2 |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | df-nul 3334 | . . . 4 | |
2 | 1 | eleq2i 2184 | . . 3 |
3 | eldif 3050 | . . 3 | |
4 | pm3.24 667 | . . . 4 | |
5 | eqid 2117 | . . . . 5 | |
6 | 5 | notnoti 619 | . . . 4 |
7 | 4, 6 | 2false 675 | . . 3 |
8 | 2, 3, 7 | 3bitri 205 | . 2 |
9 | 8 | abbi2i 2232 | 1 |
Colors of variables: wff set class |
Syntax hints: wn 3 wa 103 wceq 1316 wcel 1465 cab 2103 cvv 2660 cdif 3038 c0 3333 |
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-17 1491 ax-i9 1495 ax-ial 1499 ax-i5r 1500 ax-ext 2099 |
This theorem depends on definitions: df-bi 116 df-tru 1319 df-nf 1422 df-sb 1721 df-clab 2104 df-cleq 2110 df-clel 2113 df-nfc 2247 df-v 2662 df-dif 3043 df-nul 3334 |
This theorem is referenced by: dfnul3 3336 rab0 3361 iotanul 5073 |
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