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Mirrors > Home > ILE Home > Th. List > 1pi | Unicode version |
Description: Ordinal 'one' is a positive integer. (Contributed by NM, 29-Oct-1995.) |
Ref | Expression |
---|---|
1pi |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | 1onn 6424 | . 2 | |
2 | 1n0 6337 | . 2 | |
3 | elni 7140 | . 2 | |
4 | 1, 2, 3 | mpbir2an 927 | 1 |
Colors of variables: wff set class |
Syntax hints: wcel 1481 wne 2309 c0 3368 com 4512 c1o 6314 cnpi 7104 |
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-ne 2310 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-ni 7136 |
This theorem is referenced by: mulidpi 7150 1lt2pi 7172 nlt1pig 7173 indpi 7174 1nq 7198 1qec 7220 mulidnq 7221 1lt2nq 7238 archnqq 7249 prarloclemarch 7250 prarloclemarch2 7251 nnnq 7254 ltnnnq 7255 nq0m0r 7288 nq0a0 7289 addpinq1 7296 nq02m 7297 prarloclemlt 7325 prarloclemlo 7326 prarloclemn 7331 prarloclemcalc 7334 nqprm 7374 caucvgprlemm 7500 caucvgprprlemml 7526 caucvgprprlemmu 7527 caucvgsrlemasr 7622 caucvgsr 7634 nntopi 7726 |
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