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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 7448 | . 2 ⊢ 2𝑜 = suc 1𝑜 | |
2 | nsuceq0 5722 | . 2 ⊢ suc 1𝑜 ≠ ∅ | |
3 | 1, 2 | eqnetri 2852 | 1 ⊢ 2𝑜 ≠ ∅ |
Colors of variables: wff setvar class |
Syntax hints: ≠ wne 2780 ∅c0 3874 suc csuc 5642 1𝑜c1o 7440 2𝑜c2o 7441 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1713 ax-4 1728 ax-5 1827 ax-6 1875 ax-7 1922 ax-10 2006 ax-11 2021 ax-12 2034 ax-13 2234 ax-ext 2590 ax-nul 4717 |
This theorem depends on definitions: df-bi 196 df-or 384 df-an 385 df-tru 1478 df-ex 1696 df-nf 1701 df-sb 1868 df-clab 2597 df-cleq 2603 df-clel 2606 df-nfc 2740 df-ne 2782 df-v 3175 df-dif 3543 df-un 3545 df-nul 3875 df-sn 4126 df-suc 5646 df-2o 7448 |
This theorem is referenced by: snnen2o 8034 pmtrfmvdn0 17705 pmtrsn 17762 efgrcl 17951 sltval2 31053 sltintdifex 31060 onint1 31618 1oequni2o 32392 finxpreclem4 32407 finxp3o 32413 frlmpwfi 36686 clsk1indlem1 37363 |
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