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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 8106 | . 2 ⊢ 3o = suc 2o | |
2 | df2o3 8119 | . . . 4 ⊢ 2o = {∅, 1o} | |
3 | 2 | uneq1i 4137 | . . 3 ⊢ (2o ∪ {2o}) = ({∅, 1o} ∪ {2o}) |
4 | df-suc 6199 | . . 3 ⊢ suc 2o = (2o ∪ {2o}) | |
5 | df-tp 4574 | . . 3 ⊢ {∅, 1o, 2o} = ({∅, 1o} ∪ {2o}) | |
6 | 3, 4, 5 | 3eqtr4i 2856 | . 2 ⊢ suc 2o = {∅, 1o, 2o} |
7 | 1, 6 | eqtri 2846 | 1 ⊢ 3o = {∅, 1o, 2o} |
Colors of variables: wff setvar class |
Syntax hints: = wceq 1537 ∪ cun 3936 ∅c0 4293 {csn 4569 {cpr 4571 {ctp 4573 suc csuc 6195 1oc1o 8097 2oc2o 8098 3oc3o 8099 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1796 ax-4 1810 ax-5 1911 ax-6 1970 ax-7 2015 ax-8 2116 ax-9 2124 ax-10 2145 ax-11 2161 ax-12 2177 ax-ext 2795 |
This theorem depends on definitions: df-bi 209 df-an 399 df-or 844 df-tru 1540 df-ex 1781 df-nf 1785 df-sb 2070 df-clab 2802 df-cleq 2816 df-clel 2895 df-nfc 2965 df-v 3498 df-dif 3941 df-un 3943 df-nul 4294 df-pr 4572 df-tp 4574 df-suc 6199 df-1o 8104 df-2o 8105 df-3o 8106 |
This theorem is referenced by: clsk1indlem4 40401 clsk1indlem1 40402 |
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