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Mirrors > Home > MPE Home > Th. List > 2on0 | Structured version Visualization version GIF version |
Description: Ordinal two is not zero. (Contributed by Scott Fenton, 17-Jun-2011.) |
Ref | Expression |
---|---|
2on0 | ⊢ 2o ≠ ∅ |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | df-2o 8506 | . 2 ⊢ 2o = suc 1o | |
2 | nsuceq0 6469 | . 2 ⊢ suc 1o ≠ ∅ | |
3 | 1, 2 | eqnetri 3009 | 1 ⊢ 2o ≠ ∅ |
Colors of variables: wff setvar class |
Syntax hints: ≠ wne 2938 ∅c0 4339 suc csuc 6388 1oc1o 8498 2oc2o 8499 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1792 ax-4 1806 ax-5 1908 ax-6 1965 ax-7 2005 ax-8 2108 ax-9 2116 ax-ext 2706 ax-nul 5312 |
This theorem depends on definitions: df-bi 207 df-an 396 df-or 848 df-tru 1540 df-fal 1550 df-ex 1777 df-sb 2063 df-clab 2713 df-cleq 2727 df-clel 2814 df-ne 2939 df-v 3480 df-dif 3966 df-un 3968 df-nul 4340 df-sn 4632 df-suc 6392 df-2o 8506 |
This theorem is referenced by: ord2eln012 8534 snnen2oOLD 9262 snnen2o 9271 1sdom2 9274 1sdom2dom 9281 pmtrfmvdn0 19495 pmtrsn 19552 efgrcl 19748 sltval2 27716 sltintdifex 27721 nogt01o 27756 noinfbnd1lem5 27787 noinfbnd2lem1 27790 goaln0 35378 goalr 35382 fmla0disjsuc 35383 onint1 36432 1oequni2o 37351 finxpreclem4 37377 finxp3o 37383 frlmpwfi 43087 clsk1indlem1 44035 |
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