| Intuitionistic Logic Explorer |
< Previous
Next >
Nearby theorems |
||
| 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 6605 |
. 2
| |
| 2 | 1n0 6517 |
. 2
| |
| 3 | elni 7420 |
. 2
| |
| 4 | 1, 2, 3 | mpbir2an 944 |
1
|
| 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 615 ax-in2 616 ax-io 710 ax-5 1469 ax-7 1470 ax-gen 1471 ax-ie1 1515 ax-ie2 1516 ax-8 1526 ax-10 1527 ax-11 1528 ax-i12 1529 ax-bndl 1531 ax-4 1532 ax-17 1548 ax-i9 1552 ax-ial 1556 ax-i5r 1557 ax-13 2177 ax-14 2178 ax-ext 2186 ax-sep 4161 ax-nul 4169 ax-pow 4217 ax-pr 4252 ax-un 4479 |
| This theorem depends on definitions: df-bi 117 df-3an 982 df-tru 1375 df-nf 1483 df-sb 1785 df-clab 2191 df-cleq 2197 df-clel 2200 df-nfc 2336 df-ne 2376 df-ral 2488 df-rex 2489 df-v 2773 df-dif 3167 df-un 3169 df-in 3171 df-ss 3178 df-nul 3460 df-pw 3617 df-sn 3638 df-pr 3639 df-uni 3850 df-int 3885 df-suc 4417 df-iom 4638 df-1o 6501 df-ni 7416 |
| This theorem is referenced by: mulidpi 7430 1lt2pi 7452 nlt1pig 7453 indpi 7454 1nq 7478 1qec 7500 mulidnq 7501 1lt2nq 7518 archnqq 7529 prarloclemarch 7530 prarloclemarch2 7531 nnnq 7534 ltnnnq 7535 nq0m0r 7568 nq0a0 7569 addpinq1 7576 nq02m 7577 prarloclemlt 7605 prarloclemlo 7606 prarloclemn 7611 prarloclemcalc 7614 nqprm 7654 caucvgprlemm 7780 caucvgprprlemml 7806 caucvgprprlemmu 7807 caucvgsrlemasr 7902 caucvgsr 7914 nntopi 8006 |
| Copyright terms: Public domain | W3C validator |