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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 7460 | . 2 ⊢ 2𝑜 = {∅, 1𝑜} | |
2 | df1o2 7459 | . . 3 ⊢ 1𝑜 = {∅} | |
3 | 2 | preq2i 4216 | . 2 ⊢ {∅, 1𝑜} = {∅, {∅}} |
4 | 1, 3 | eqtri 2632 | 1 ⊢ 2𝑜 = {∅, {∅}} |
Colors of variables: wff setvar class |
Syntax hints: = wceq 1475 ∅c0 3874 {csn 4125 {cpr 4127 1𝑜c1o 7440 2𝑜c2o 7441 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1713 ax-4 1728 ax-5 1827 ax-6 1875 ax-7 1922 ax-10 2006 ax-11 2021 ax-12 2034 ax-13 2234 ax-ext 2590 |
This theorem depends on definitions: df-bi 196 df-or 384 df-an 385 df-tru 1478 df-ex 1696 df-nf 1701 df-sb 1868 df-clab 2597 df-cleq 2603 df-clel 2606 df-nfc 2740 df-v 3175 df-dif 3543 df-un 3545 df-nul 3875 df-sn 4126 df-pr 4128 df-suc 5646 df-1o 7447 df-2o 7448 |
This theorem is referenced by: 2dom 7915 pw2eng 7951 pwcda1 8899 canthp1lem1 9353 pr0hash2ex 13057 hashpw 13083 znidomb 19729 ssoninhaus 31617 onint1 31618 pw2f1ocnv 36622 df3o3 37343 |
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