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Mirrors > Home > NFE Home > Th. List > 0cex | Unicode version |
Description: Cardinal zero is a set. (Contributed by SF, 14-Jan-2015.) |
Ref | Expression |
---|---|
0cex | 0c |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | df-0c 4377 | . 2 0c | |
2 | snex 4111 | . 2 | |
3 | 1, 2 | eqeltri 2423 | 1 0c |
Colors of variables: wff setvar class |
Syntax hints: wcel 1710 cvv 2859 c0 3550 csn 3737 0cc0c 4374 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1546 ax-5 1557 ax-17 1616 ax-9 1654 ax-8 1675 ax-6 1729 ax-7 1734 ax-11 1746 ax-12 1925 ax-ext 2334 ax-nin 4078 ax-sn 4087 |
This theorem depends on definitions: df-bi 177 df-or 359 df-an 360 df-nan 1288 df-tru 1319 df-ex 1542 df-nf 1545 df-sb 1649 df-clab 2340 df-cleq 2346 df-clel 2349 df-nfc 2478 df-ne 2518 df-v 2861 df-nin 3211 df-compl 3212 df-in 3213 df-un 3214 df-dif 3215 df-ss 3259 df-nul 3551 df-sn 3741 df-0c 4377 |
This theorem is referenced by: peano1 4402 findsd 4410 ltfintri 4466 0ceven 4505 0cnelphi 4597 proj1op 4600 proj2op 4601 dfnnc3 5885 ce0nn 6180 lec0cg 6198 frecxp 6314 dmfrec 6316 fnfreclem2 6318 fnfreclem3 6319 |
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