![]() |
Metamath Proof Explorer |
< Previous
Next >
Nearby theorems |
|
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 8470 | . 2 ⊢ 2o = {∅, 1o} | |
2 | df1o2 8469 | . . 3 ⊢ 1o = {∅} | |
3 | 2 | preq2i 4740 | . 2 ⊢ {∅, 1o} = {∅, {∅}} |
4 | 1, 3 | eqtri 2760 | 1 ⊢ 2o = {∅, {∅}} |
Colors of variables: wff setvar class |
Syntax hints: = wceq 1541 ∅c0 4321 {csn 4627 {cpr 4629 1oc1o 8455 2oc2o 8456 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1797 ax-4 1811 ax-5 1913 ax-6 1971 ax-7 2011 ax-8 2108 ax-9 2116 ax-ext 2703 |
This theorem depends on definitions: df-bi 206 df-an 397 df-or 846 df-tru 1544 df-fal 1554 df-ex 1782 df-sb 2068 df-clab 2710 df-cleq 2724 df-clel 2810 df-v 3476 df-dif 3950 df-un 3952 df-nul 4322 df-sn 4628 df-pr 4630 df-suc 6367 df-1o 8462 df-2o 8463 |
This theorem is referenced by: 2dom 9026 pw2eng 9074 pwdju1 10181 canthp1lem1 10643 pr0hash2ex 14364 hashpw 14392 cat1 18043 znidomb 21108 ssoninhaus 35321 onint1 35322 pw2f1ocnv 41761 2omomeqom 42038 df3o3 42049 setc2othin 47629 |
Copyright terms: Public domain | W3C validator |