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| Description: Alternate definition of the empty set. Definition 5.14 of [TakeutiZaring] p. 20. |
| Ref | Expression |
|---|---|
| dfnul2 |
|
| Step | Hyp | Ref | Expression |
|---|---|---|---|
| 1 | df-nul 2331 |
. . . 4
| |
| 2 | 1 | eleq2i 1579 |
. . 3
|
| 3 | eldif 2107 |
. . 3
| |
| 4 | eqid 1516 |
. . . . 5
| |
| 5 | pm3.24 660 |
. . . . 5
| |
| 6 | 4, 5 | 2th 721 |
. . . 4
|
| 7 | 6 | con2bii 219 |
. . 3
|
| 8 | 2, 3, 7 | 3bitri 175 |
. 2
|
| 9 | 8 | abbi2i 1615 |
1
|
| Colors of variables: wff set class |
| Syntax hints: |
| This theorem is referenced by: dfnul3 2333 noel 2334 dm0 3411 avril1 9035 |
| This theorem was proved from axioms: ax-1 4 ax-2 5 ax-3 6 ax-mp 7 ax-7 995 ax-gen 996 ax-8 997 ax-10 999 ax-12 1001 ax-17 1004 ax-4 1006 ax-5o 1008 ax-6o 1011 ax-9o 1156 ax-10o 1174 ax-16 1244 ax-11o 1252 ax-ext 1498 |
| This theorem depends on definitions: df-bi 145 df-or 222 df-an 223 df-ex 1014 df-sb 1206 df-clab 1504 df-cleq 1509 df-clel 1512 df-v 1856 df-dif 2099 df-nul 2331 |