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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 3225 | . . . 4 | |
2 | 1 | eleq2i 2104 | . . 3 |
3 | eldif 2927 | . . 3 | |
4 | pm3.24 627 | . . . 4 | |
5 | eqid 2040 | . . . . 5 | |
6 | 5 | notnoti 574 | . . . 4 |
7 | 4, 6 | 2false 617 | . . 3 |
8 | 2, 3, 7 | 3bitri 195 | . 2 |
9 | 8 | abbi2i 2152 | 1 |
Colors of variables: wff set class |
Syntax hints: wn 3 wa 97 wceq 1243 wcel 1393 cab 2026 cvv 2557 cdif 2914 c0 3224 |
This theorem was proved from axioms: ax-1 5 ax-2 6 ax-mp 7 ax-ia1 99 ax-ia2 100 ax-ia3 101 ax-in1 544 ax-in2 545 ax-io 630 ax-5 1336 ax-7 1337 ax-gen 1338 ax-ie1 1382 ax-ie2 1383 ax-8 1395 ax-10 1396 ax-11 1397 ax-i12 1398 ax-bndl 1399 ax-4 1400 ax-17 1419 ax-i9 1423 ax-ial 1427 ax-i5r 1428 ax-ext 2022 |
This theorem depends on definitions: df-bi 110 df-tru 1246 df-nf 1350 df-sb 1646 df-clab 2027 df-cleq 2033 df-clel 2036 df-nfc 2167 df-v 2559 df-dif 2920 df-nul 3225 |
This theorem is referenced by: dfnul3 3227 rab0 3246 iotanul 4882 |
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