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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 8094 | . 2 ⊢ 2o = suc 1o | |
2 | nsuceq0 6265 | . 2 ⊢ suc 1o ≠ ∅ | |
3 | 1, 2 | eqnetri 3086 | 1 ⊢ 2o ≠ ∅ |
Colors of variables: wff setvar class |
Syntax hints: ≠ wne 3016 ∅c0 4290 suc csuc 6187 1oc1o 8086 2oc2o 8087 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1787 ax-4 1801 ax-5 1902 ax-6 1961 ax-7 2006 ax-8 2107 ax-9 2115 ax-10 2136 ax-11 2151 ax-12 2167 ax-ext 2793 ax-nul 5202 |
This theorem depends on definitions: df-bi 208 df-an 397 df-or 842 df-tru 1531 df-ex 1772 df-nf 1776 df-sb 2061 df-clab 2800 df-cleq 2814 df-clel 2893 df-nfc 2963 df-ne 3017 df-v 3497 df-dif 3938 df-un 3940 df-nul 4291 df-sn 4560 df-suc 6191 df-2o 8094 |
This theorem is referenced by: snnen2o 8696 pmtrfmvdn0 18521 pmtrsn 18578 efgrcl 18772 goaln0 32538 goalr 32542 fmla0disjsuc 32543 sltval2 33061 sltintdifex 33066 onint1 33695 1oequni2o 34532 finxpreclem4 34558 finxp3o 34564 frlmpwfi 39578 clsk1indlem1 40275 |
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