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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 |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | df-2o 6396 | . 2 | |
2 | 1onn 6499 | . . 3 | |
3 | peano2 4579 | . . 3 | |
4 | 2, 3 | ax-mp 5 | . 2 |
5 | 1, 4 | eqeltri 2243 | 1 |
Colors of variables: wff set class |
Syntax hints: wcel 2141 csuc 4350 com 4574 c1o 6388 c2o 6389 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-ia1 105 ax-ia2 106 ax-ia3 107 ax-in1 609 ax-in2 610 ax-io 704 ax-5 1440 ax-7 1441 ax-gen 1442 ax-ie1 1486 ax-ie2 1487 ax-8 1497 ax-10 1498 ax-11 1499 ax-i12 1500 ax-bndl 1502 ax-4 1503 ax-17 1519 ax-i9 1523 ax-ial 1527 ax-i5r 1528 ax-13 2143 ax-14 2144 ax-ext 2152 ax-sep 4107 ax-nul 4115 ax-pow 4160 ax-pr 4194 ax-un 4418 |
This theorem depends on definitions: df-bi 116 df-3an 975 df-tru 1351 df-nf 1454 df-sb 1756 df-clab 2157 df-cleq 2163 df-clel 2166 df-nfc 2301 df-ral 2453 df-rex 2454 df-v 2732 df-dif 3123 df-un 3125 df-in 3127 df-ss 3134 df-nul 3415 df-pw 3568 df-sn 3589 df-pr 3590 df-uni 3797 df-int 3832 df-suc 4356 df-iom 4575 df-1o 6395 df-2o 6396 |
This theorem is referenced by: 3onn 6501 2ssom 6503 nn2m 6506 pw1fin 6888 nninfex 7098 infnninfOLD 7101 nnnninf 7102 isomnimap 7113 enomnilem 7114 fodjuf 7121 ismkvmap 7130 ismkvnex 7131 enmkvlem 7137 iswomnimap 7142 enwomnilem 7145 nninfdcinf 7147 nninfwlporlem 7149 nninfwlpoimlemg 7151 exmidonfinlem 7170 exmidfodomrlemr 7179 exmidfodomrlemrALT 7180 pw1ne3 7207 3nsssucpw1 7213 prarloclemarch2 7381 nq02m 7427 prarloclemlt 7455 prarloclemlo 7456 prarloclem3 7459 prarloclemn 7461 prarloclem5 7462 prarloclemcalc 7464 hash3 10748 unct 12397 2o01f 14029 pwle2 14031 pwf1oexmid 14032 subctctexmid 14034 0nninf 14037 nnsf 14038 nninfsellemdc 14043 nninfself 14046 nninffeq 14053 isomninnlem 14062 iswomninnlem 14081 ismkvnnlem 14084 |
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