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Mirrors > Home > ILE Home > Th. List > pinn | Unicode version |
Description: A positive integer is a natural number. (Contributed by NM, 15-Aug-1995.) |
Ref | Expression |
---|---|
pinn |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | df-ni 7302 |
. . 3
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2 | difss 3261 |
. . 3
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3 | 1, 2 | eqsstri 3187 |
. 2
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4 | 3 | sseli 3151 |
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-ext 2159 |
This theorem depends on definitions: df-bi 117 df-tru 1356 df-nf 1461 df-sb 1763 df-clab 2164 df-cleq 2170 df-clel 2173 df-nfc 2308 df-v 2739 df-dif 3131 df-in 3135 df-ss 3142 df-ni 7302 |
This theorem is referenced by: pion 7308 piord 7309 elni2 7312 mulidpi 7316 ltsopi 7318 pitric 7319 pitri3or 7320 ltdcpi 7321 addclpi 7325 mulclpi 7326 addcompig 7327 addasspig 7328 mulcompig 7329 mulasspig 7330 distrpig 7331 addcanpig 7332 mulcanpig 7333 addnidpig 7334 ltexpi 7335 ltapig 7336 ltmpig 7337 nnppipi 7341 enqdc 7359 archnqq 7415 prarloclemarch2 7417 enq0enq 7429 enq0sym 7430 enq0ref 7431 enq0tr 7432 nqnq0pi 7436 nqnq0 7439 addcmpblnq0 7441 mulcmpblnq0 7442 mulcanenq0ec 7443 addclnq0 7449 nqpnq0nq 7451 nqnq0a 7452 nqnq0m 7453 nq0m0r 7454 nq0a0 7455 nnanq0 7456 distrnq0 7457 mulcomnq0 7458 addassnq0lemcl 7459 addassnq0 7460 nq02m 7463 prarloclemlt 7491 prarloclemn 7497 |
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