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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 8106 | . 2 ⊢ 2o = {∅, 1o} | |
2 | df1o2 8105 | . . 3 ⊢ 1o = {∅} | |
3 | 2 | preq2i 4665 | . 2 ⊢ {∅, 1o} = {∅, {∅}} |
4 | 1, 3 | eqtri 2841 | 1 ⊢ 2o = {∅, {∅}} |
Colors of variables: wff setvar class |
Syntax hints: = wceq 1528 ∅c0 4288 {csn 4557 {cpr 4559 1oc1o 8084 2oc2o 8085 |
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 2790 |
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 2797 df-cleq 2811 df-clel 2890 df-nfc 2960 df-v 3494 df-dif 3936 df-un 3938 df-nul 4289 df-sn 4558 df-pr 4560 df-suc 6190 df-1o 8091 df-2o 8092 |
This theorem is referenced by: 2dom 8570 pw2eng 8611 pwdju1 9604 canthp1lem1 10062 pr0hash2ex 13757 hashpw 13785 znidomb 20636 ssoninhaus 33693 onint1 33694 pw2f1ocnv 39512 df3o3 40253 |
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