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Mirrors > Home > ILE Home > Th. List > nlt1pig | Unicode version |
Description: No positive integer is less than one. (Contributed by Jim Kingdon, 31-Aug-2019.) |
Ref | Expression |
---|---|
nlt1pig |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | elni 7306 |
. . 3
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2 | 1 | simprbi 275 |
. 2
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3 | noel 3426 |
. . . . 5
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4 | 1pi 7313 |
. . . . . . . . 9
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5 | ltpiord 7317 |
. . . . . . . . 9
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6 | 4, 5 | mpan2 425 |
. . . . . . . 8
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7 | df-1o 6416 |
. . . . . . . . . 10
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8 | 7 | eleq2i 2244 |
. . . . . . . . 9
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9 | elsucg 4404 |
. . . . . . . . 9
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10 | 8, 9 | bitrid 192 |
. . . . . . . 8
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11 | 6, 10 | bitrd 188 |
. . . . . . 7
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12 | 11 | biimpa 296 |
. . . . . 6
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13 | 12 | ord 724 |
. . . . 5
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14 | 3, 13 | mpi 15 |
. . . 4
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15 | 14 | ex 115 |
. . 3
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16 | 15 | necon3ad 2389 |
. 2
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17 | 2, 16 | mpd 13 |
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 4121 ax-nul 4129 ax-pow 4174 ax-pr 4209 ax-un 4433 |
This theorem depends on definitions: df-bi 117 df-3an 980 df-tru 1356 df-nf 1461 df-sb 1763 df-eu 2029 df-mo 2030 df-clab 2164 df-cleq 2170 df-clel 2173 df-nfc 2308 df-ne 2348 df-ral 2460 df-rex 2461 df-v 2739 df-dif 3131 df-un 3133 df-in 3135 df-ss 3142 df-nul 3423 df-pw 3577 df-sn 3598 df-pr 3599 df-op 3601 df-uni 3810 df-int 3845 df-br 4004 df-opab 4065 df-eprel 4289 df-suc 4371 df-iom 4590 df-xp 4632 df-1o 6416 df-ni 7302 df-lti 7305 |
This theorem is referenced by: caucvgsr 7800 |
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