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Mirrors > Home > ILE Home > Th. List > 1onn | Unicode version |
Description: One is a natural number. (Contributed by NM, 29-Oct-1995.) |
Ref | Expression |
---|---|
1onn |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | df-1o 6281 | . 2 | |
2 | peano1 4478 | . . 3 | |
3 | peano2 4479 | . . 3 | |
4 | 2, 3 | ax-mp 5 | . 2 |
5 | 1, 4 | eqeltri 2190 | 1 |
Colors of variables: wff set class |
Syntax hints: wcel 1465 c0 3333 csuc 4257 com 4474 c1o 6274 |
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 588 ax-in2 589 ax-io 683 ax-5 1408 ax-7 1409 ax-gen 1410 ax-ie1 1454 ax-ie2 1455 ax-8 1467 ax-10 1468 ax-11 1469 ax-i12 1470 ax-bndl 1471 ax-4 1472 ax-13 1476 ax-14 1477 ax-17 1491 ax-i9 1495 ax-ial 1499 ax-i5r 1500 ax-ext 2099 ax-sep 4016 ax-nul 4024 ax-pow 4068 ax-pr 4101 ax-un 4325 |
This theorem depends on definitions: df-bi 116 df-3an 949 df-tru 1319 df-nf 1422 df-sb 1721 df-clab 2104 df-cleq 2110 df-clel 2113 df-nfc 2247 df-ral 2398 df-rex 2399 df-v 2662 df-dif 3043 df-un 3045 df-in 3047 df-ss 3054 df-nul 3334 df-pw 3482 df-sn 3503 df-pr 3504 df-uni 3707 df-int 3742 df-suc 4263 df-iom 4475 df-1o 6281 |
This theorem is referenced by: 2onn 6385 nnm2 6389 nnaordex 6391 snfig 6676 snnen2og 6721 1nen2 6723 unfiexmid 6774 en1eqsn 6804 omp1eomlem 6947 fodjum 6986 fodju0 6987 en2eleq 7019 en2other2 7020 exmidfodomrlemr 7026 exmidfodomrlemrALT 7027 1pi 7091 1lt2pi 7116 archnqq 7193 nq0m0r 7232 nq02m 7241 prarloclemlt 7269 prarloclemlo 7270 1tonninf 10181 hash2 10526 pwle2 13120 peano3nninf 13128 nninfall 13131 nninfsellemdc 13133 nninfsellemeq 13137 nninfsellemeqinf 13139 nninffeq 13143 sbthom 13148 isomninnlem 13152 |
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