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Mirrors > Home > MPE Home > Th. List > df2o2 | Structured version Visualization version GIF version |
Description: Expanded value of the ordinal number 2. (Contributed by NM, 29-Jan-2004.) |
Ref | Expression |
---|---|
df2o2 | ⊢ 2o = {∅, {∅}} |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | df2o3 8217 | . 2 ⊢ 2o = {∅, 1o} | |
2 | df1o2 8214 | . . 3 ⊢ 1o = {∅} | |
3 | 2 | preq2i 4653 | . 2 ⊢ {∅, 1o} = {∅, {∅}} |
4 | 1, 3 | eqtri 2765 | 1 ⊢ 2o = {∅, {∅}} |
Colors of variables: wff setvar class |
Syntax hints: = wceq 1543 ∅c0 4237 {csn 4541 {cpr 4543 1oc1o 8195 2oc2o 8196 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1803 ax-4 1817 ax-5 1918 ax-6 1976 ax-7 2016 ax-8 2112 ax-9 2120 ax-ext 2708 |
This theorem depends on definitions: df-bi 210 df-an 400 df-or 848 df-tru 1546 df-fal 1556 df-ex 1788 df-sb 2071 df-clab 2715 df-cleq 2729 df-clel 2816 df-v 3410 df-dif 3869 df-un 3871 df-nul 4238 df-sn 4542 df-pr 4544 df-suc 6219 df-1o 8202 df-2o 8203 |
This theorem is referenced by: 2dom 8707 pw2eng 8751 pwdju1 9804 canthp1lem1 10266 pr0hash2ex 13975 hashpw 14003 cat1 17603 znidomb 20526 ssoninhaus 34374 onint1 34375 pw2f1ocnv 40562 df3o3 41312 setc2othin 46010 |
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