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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 8499 | . 2 ⊢ 2o = suc 1o | |
2 | nsuceq0 6461 | . 2 ⊢ suc 1o ≠ ∅ | |
3 | 1, 2 | eqnetri 3001 | 1 ⊢ 2o ≠ ∅ |
Colors of variables: wff setvar class |
Syntax hints: ≠ wne 2930 ∅c0 4325 suc csuc 6380 1oc1o 8491 2oc2o 8492 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1790 ax-4 1804 ax-5 1906 ax-6 1964 ax-7 2004 ax-8 2101 ax-9 2109 ax-ext 2697 ax-nul 5313 |
This theorem depends on definitions: df-bi 206 df-an 395 df-or 846 df-tru 1537 df-fal 1547 df-ex 1775 df-sb 2061 df-clab 2704 df-cleq 2718 df-clel 2803 df-ne 2931 df-v 3464 df-dif 3950 df-un 3952 df-nul 4326 df-sn 4634 df-suc 6384 df-2o 8499 |
This theorem is referenced by: ord2eln012 8529 snnen2oOLD 9263 snnen2o 9273 1sdom2 9276 1sdom2dom 9283 pmtrfmvdn0 19462 pmtrsn 19519 efgrcl 19715 sltval2 27689 sltintdifex 27694 nogt01o 27729 noinfbnd1lem5 27760 noinfbnd2lem1 27763 goaln0 35223 goalr 35227 fmla0disjsuc 35228 onint1 36163 1oequni2o 37077 finxpreclem4 37103 finxp3o 37109 frlmpwfi 42777 clsk1indlem1 43730 |
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