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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 6322 |
. 2
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2 | 1onn 6424 |
. . 3
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3 | peano2 4517 |
. . 3
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4 | 2, 3 | ax-mp 5 |
. 2
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5 | 1, 4 | eqeltri 2213 |
1
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Colors of variables: wff set class |
Syntax hints: ![]() ![]() ![]() ![]() ![]() |
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 604 ax-in2 605 ax-io 699 ax-5 1424 ax-7 1425 ax-gen 1426 ax-ie1 1470 ax-ie2 1471 ax-8 1483 ax-10 1484 ax-11 1485 ax-i12 1486 ax-bndl 1487 ax-4 1488 ax-13 1492 ax-14 1493 ax-17 1507 ax-i9 1511 ax-ial 1515 ax-i5r 1516 ax-ext 2122 ax-sep 4054 ax-nul 4062 ax-pow 4106 ax-pr 4139 ax-un 4363 |
This theorem depends on definitions: df-bi 116 df-3an 965 df-tru 1335 df-nf 1438 df-sb 1737 df-clab 2127 df-cleq 2133 df-clel 2136 df-nfc 2271 df-ral 2422 df-rex 2423 df-v 2691 df-dif 3078 df-un 3080 df-in 3082 df-ss 3089 df-nul 3369 df-pw 3517 df-sn 3538 df-pr 3539 df-uni 3745 df-int 3780 df-suc 4301 df-iom 4513 df-1o 6321 df-2o 6322 |
This theorem is referenced by: 3onn 6426 nn2m 6430 isomnimap 7017 enomnilem 7018 fodjuf 7025 infnninf 7030 nnnninf 7031 ismkvmap 7036 ismkvnex 7037 enmkvlem 7043 iswomnimap 7048 enwomnilem 7050 exmidonfinlem 7066 exmidfodomrlemr 7075 exmidfodomrlemrALT 7076 prarloclemarch2 7251 nq02m 7297 prarloclemlt 7325 prarloclemlo 7326 prarloclem3 7329 prarloclemn 7331 prarloclem5 7332 prarloclemcalc 7334 hash3 10591 unct 11991 2o01f 13364 pwle2 13366 pwf1oexmid 13367 subctctexmid 13369 0nninf 13372 nnsf 13374 nninfex 13380 nninfsellemdc 13381 nninfself 13384 nninffeq 13391 isomninnlem 13400 iswomninnlem 13417 ismkvnnlem 13419 |
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