Intuitionistic Logic Explorer |
< Previous
Next >
Nearby theorems |
||
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 7236 | . . 3 | |
2 | difss 3243 | . . 3 | |
3 | 1, 2 | eqsstri 3169 | . 2 |
4 | 3 | sseli 3133 | 1 |
Colors of variables: wff set class |
Syntax hints: wi 4 wcel 2135 cdif 3108 c0 3404 csn 3570 com 4561 cnpi 7204 |
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 1434 ax-7 1435 ax-gen 1436 ax-ie1 1480 ax-ie2 1481 ax-8 1491 ax-10 1492 ax-11 1493 ax-i12 1494 ax-bndl 1496 ax-4 1497 ax-17 1513 ax-i9 1517 ax-ial 1521 ax-i5r 1522 ax-ext 2146 |
This theorem depends on definitions: df-bi 116 df-tru 1345 df-nf 1448 df-sb 1750 df-clab 2151 df-cleq 2157 df-clel 2160 df-nfc 2295 df-v 2723 df-dif 3113 df-in 3117 df-ss 3124 df-ni 7236 |
This theorem is referenced by: pion 7242 piord 7243 elni2 7246 mulidpi 7250 ltsopi 7252 pitric 7253 pitri3or 7254 ltdcpi 7255 addclpi 7259 mulclpi 7260 addcompig 7261 addasspig 7262 mulcompig 7263 mulasspig 7264 distrpig 7265 addcanpig 7266 mulcanpig 7267 addnidpig 7268 ltexpi 7269 ltapig 7270 ltmpig 7271 nnppipi 7275 enqdc 7293 archnqq 7349 prarloclemarch2 7351 enq0enq 7363 enq0sym 7364 enq0ref 7365 enq0tr 7366 nqnq0pi 7370 nqnq0 7373 addcmpblnq0 7375 mulcmpblnq0 7376 mulcanenq0ec 7377 addclnq0 7383 nqpnq0nq 7385 nqnq0a 7386 nqnq0m 7387 nq0m0r 7388 nq0a0 7389 nnanq0 7390 distrnq0 7391 mulcomnq0 7392 addassnq0lemcl 7393 addassnq0 7394 nq02m 7397 prarloclemlt 7425 prarloclemn 7431 |
Copyright terms: Public domain | W3C validator |