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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 7718 | . 2 ⊢ 2𝑜 = suc 1𝑜 | |
2 | nsuceq0 5947 | . 2 ⊢ suc 1𝑜 ≠ ∅ | |
3 | 1, 2 | eqnetri 3013 | 1 ⊢ 2𝑜 ≠ ∅ |
Colors of variables: wff setvar class |
Syntax hints: ≠ wne 2943 ∅c0 4063 suc csuc 5867 1𝑜c1o 7710 2𝑜c2o 7711 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1870 ax-4 1885 ax-5 1991 ax-6 2057 ax-7 2093 ax-9 2154 ax-10 2174 ax-11 2190 ax-12 2203 ax-13 2408 ax-ext 2751 ax-nul 4924 |
This theorem depends on definitions: df-bi 197 df-an 383 df-or 837 df-tru 1634 df-ex 1853 df-nf 1858 df-sb 2050 df-clab 2758 df-cleq 2764 df-clel 2767 df-nfc 2902 df-ne 2944 df-v 3353 df-dif 3726 df-un 3728 df-nul 4064 df-sn 4318 df-suc 5871 df-2o 7718 |
This theorem is referenced by: snnen2o 8309 pmtrfmvdn0 18089 pmtrsn 18146 efgrcl 18335 sltval2 32146 sltintdifex 32151 onint1 32785 1oequni2o 33552 finxpreclem4 33567 finxp3o 33573 frlmpwfi 38192 clsk1indlem1 38867 |
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