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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 |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | df-ni 7112 | . . 3 | |
2 | difss 3202 | . . 3 | |
3 | 1, 2 | eqsstri 3129 | . 2 |
4 | 3 | sseli 3093 | 1 |
Colors of variables: wff set class |
Syntax hints: wi 4 wcel 1480 cdif 3068 c0 3363 csn 3527 com 4504 cnpi 7080 |
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 603 ax-in2 604 ax-io 698 ax-5 1423 ax-7 1424 ax-gen 1425 ax-ie1 1469 ax-ie2 1470 ax-8 1482 ax-10 1483 ax-11 1484 ax-i12 1485 ax-bndl 1486 ax-4 1487 ax-17 1506 ax-i9 1510 ax-ial 1514 ax-i5r 1515 ax-ext 2121 |
This theorem depends on definitions: df-bi 116 df-tru 1334 df-nf 1437 df-sb 1736 df-clab 2126 df-cleq 2132 df-clel 2135 df-nfc 2270 df-v 2688 df-dif 3073 df-in 3077 df-ss 3084 df-ni 7112 |
This theorem is referenced by: pion 7118 piord 7119 elni2 7122 mulidpi 7126 ltsopi 7128 pitric 7129 pitri3or 7130 ltdcpi 7131 addclpi 7135 mulclpi 7136 addcompig 7137 addasspig 7138 mulcompig 7139 mulasspig 7140 distrpig 7141 addcanpig 7142 mulcanpig 7143 addnidpig 7144 ltexpi 7145 ltapig 7146 ltmpig 7147 nnppipi 7151 enqdc 7169 archnqq 7225 prarloclemarch2 7227 enq0enq 7239 enq0sym 7240 enq0ref 7241 enq0tr 7242 nqnq0pi 7246 nqnq0 7249 addcmpblnq0 7251 mulcmpblnq0 7252 mulcanenq0ec 7253 addclnq0 7259 nqpnq0nq 7261 nqnq0a 7262 nqnq0m 7263 nq0m0r 7264 nq0a0 7265 nnanq0 7266 distrnq0 7267 mulcomnq0 7268 addassnq0lemcl 7269 addassnq0 7270 nq02m 7273 prarloclemlt 7301 prarloclemn 7307 |
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