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Mirrors > Home > ILE Home > Th. List > 2onn | Unicode version |
Description: The ordinal 2 is a natural number. (Contributed by NM, 28-Sep-2004.) |
Ref | Expression |
---|---|
2onn |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | df-2o 6196 |
. 2
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2 | 1onn 6293 |
. . 3
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3 | peano2 4423 |
. . 3
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4 | 2, 3 | ax-mp 7 |
. 2
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5 | 1, 4 | eqeltri 2161 |
1
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Colors of variables: wff set class |
Syntax hints: ![]() ![]() ![]() ![]() ![]() |
This theorem was proved from axioms: ax-1 5 ax-2 6 ax-mp 7 ax-ia1 105 ax-ia2 106 ax-ia3 107 ax-in1 580 ax-in2 581 ax-io 666 ax-5 1382 ax-7 1383 ax-gen 1384 ax-ie1 1428 ax-ie2 1429 ax-8 1441 ax-10 1442 ax-11 1443 ax-i12 1444 ax-bndl 1445 ax-4 1446 ax-13 1450 ax-14 1451 ax-17 1465 ax-i9 1469 ax-ial 1473 ax-i5r 1474 ax-ext 2071 ax-sep 3963 ax-nul 3971 ax-pow 4015 ax-pr 4045 ax-un 4269 |
This theorem depends on definitions: df-bi 116 df-3an 927 df-tru 1293 df-nf 1396 df-sb 1694 df-clab 2076 df-cleq 2082 df-clel 2085 df-nfc 2218 df-ral 2365 df-rex 2366 df-v 2622 df-dif 3002 df-un 3004 df-in 3006 df-ss 3013 df-nul 3288 df-pw 3435 df-sn 3456 df-pr 3457 df-uni 3660 df-int 3695 df-suc 4207 df-iom 4419 df-1o 6195 df-2o 6196 |
This theorem is referenced by: 3onn 6295 nn2m 6299 isomnimap 6854 enomnilem 6855 fodjuomnilemf 6861 infnninf 6866 nnnninf 6867 exmidfodomrlemr 6889 exmidfodomrlemrALT 6890 prarloclemarch2 7039 nq02m 7085 prarloclemlt 7113 prarloclemlo 7114 prarloclem3 7117 prarloclemn 7119 prarloclem5 7120 prarloclemcalc 7122 hash3 10282 0nninf 12165 nnsf 12167 nninfex 12173 nninfsellemdc 12174 nninfself 12177 |
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