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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 7827 | . 2 ⊢ 2o = suc 1o | |
2 | nsuceq0 6043 | . 2 ⊢ suc 1o ≠ ∅ | |
3 | 1, 2 | eqnetri 3069 | 1 ⊢ 2o ≠ ∅ |
Colors of variables: wff setvar class |
Syntax hints: ≠ wne 2999 ∅c0 4144 suc csuc 5965 1oc1o 7819 2oc2o 7820 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1896 ax-4 1910 ax-5 2011 ax-6 2077 ax-7 2114 ax-9 2175 ax-10 2194 ax-11 2209 ax-12 2222 ax-13 2391 ax-ext 2803 ax-nul 5013 |
This theorem depends on definitions: df-bi 199 df-an 387 df-or 881 df-tru 1662 df-ex 1881 df-nf 1885 df-sb 2070 df-clab 2812 df-cleq 2818 df-clel 2821 df-nfc 2958 df-ne 3000 df-v 3416 df-dif 3801 df-un 3803 df-nul 4145 df-sn 4398 df-suc 5969 df-2o 7827 |
This theorem is referenced by: snnen2o 8418 pmtrfmvdn0 18232 pmtrsn 18290 efgrcl 18479 sltval2 32348 sltintdifex 32353 onint1 32981 1oequni2o 33761 finxpreclem4 33776 finxp3o 33782 frlmpwfi 38511 clsk1indlem1 39183 |
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