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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 |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | df-1o 6419 |
. 2
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2 | peano1 4595 |
. . 3
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3 | peano2 4596 |
. . 3
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4 | 2, 3 | ax-mp 5 |
. 2
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5 | 1, 4 | eqeltri 2250 |
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 106 ax-ia2 107 ax-ia3 108 ax-in1 614 ax-in2 615 ax-io 709 ax-5 1447 ax-7 1448 ax-gen 1449 ax-ie1 1493 ax-ie2 1494 ax-8 1504 ax-10 1505 ax-11 1506 ax-i12 1507 ax-bndl 1509 ax-4 1510 ax-17 1526 ax-i9 1530 ax-ial 1534 ax-i5r 1535 ax-13 2150 ax-14 2151 ax-ext 2159 ax-sep 4123 ax-nul 4131 ax-pow 4176 ax-pr 4211 ax-un 4435 |
This theorem depends on definitions: df-bi 117 df-3an 980 df-tru 1356 df-nf 1461 df-sb 1763 df-clab 2164 df-cleq 2170 df-clel 2173 df-nfc 2308 df-ral 2460 df-rex 2461 df-v 2741 df-dif 3133 df-un 3135 df-in 3137 df-ss 3144 df-nul 3425 df-pw 3579 df-sn 3600 df-pr 3601 df-uni 3812 df-int 3847 df-suc 4373 df-iom 4592 df-1o 6419 |
This theorem is referenced by: 2onn 6524 nnm2 6529 nnaordex 6531 snfig 6816 snnen2og 6861 1nen2 6863 unfiexmid 6919 en1eqsn 6949 omp1eomlem 7095 fodjum 7146 fodju0 7147 nninfdcinf 7171 nninfwlporlemd 7172 nninfwlporlem 7173 en2eleq 7196 en2other2 7197 exmidfodomrlemr 7203 exmidfodomrlemrALT 7204 1pi 7316 1lt2pi 7341 archnqq 7418 nq0m0r 7457 nq02m 7466 prarloclemlt 7494 prarloclemlo 7495 1tonninf 10442 hash2 10794 fnpr2o 12763 fvpr1o 12766 012of 14830 pwle2 14833 peano3nninf 14841 nninfall 14843 nninfsellemdc 14844 nninfsellemeq 14848 nninfsellemeqinf 14850 nninffeq 14854 sbthom 14859 isomninnlem 14863 iswomninnlem 14882 ismkvnnlem 14885 |
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