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Mirrors > Home > MPE Home > Th. List > Mathboxes > df3o2 | Structured version Visualization version GIF version |
Description: Ordinal 3 is the triplet containing ordinals 0, 1 and 2. (Contributed by RP, 8-Jul-2021.) |
Ref | Expression |
---|---|
df3o2 | ⊢ 3o = {∅, 1o, 2o} |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | df-3o 8095 | . 2 ⊢ 3o = suc 2o | |
2 | df2o3 8108 | . . . 4 ⊢ 2o = {∅, 1o} | |
3 | 2 | uneq1i 4134 | . . 3 ⊢ (2o ∪ {2o}) = ({∅, 1o} ∪ {2o}) |
4 | df-suc 6191 | . . 3 ⊢ suc 2o = (2o ∪ {2o}) | |
5 | df-tp 4564 | . . 3 ⊢ {∅, 1o, 2o} = ({∅, 1o} ∪ {2o}) | |
6 | 3, 4, 5 | 3eqtr4i 2854 | . 2 ⊢ suc 2o = {∅, 1o, 2o} |
7 | 1, 6 | eqtri 2844 | 1 ⊢ 3o = {∅, 1o, 2o} |
Colors of variables: wff setvar class |
Syntax hints: = wceq 1528 ∪ cun 3933 ∅c0 4290 {csn 4559 {cpr 4561 {ctp 4563 suc csuc 6187 1oc1o 8086 2oc2o 8087 3oc3o 8088 |
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 |
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-v 3497 df-dif 3938 df-un 3940 df-nul 4291 df-pr 4562 df-tp 4564 df-suc 6191 df-1o 8093 df-2o 8094 df-3o 8095 |
This theorem is referenced by: clsk1indlem4 40274 clsk1indlem1 40275 |
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