![]() |
Intuitionistic Logic Explorer |
< Previous
Next >
Nearby theorems |
|
Mirrors > Home > ILE Home > Th. List > nnon | Unicode version |
Description: A natural number is an ordinal number. (Contributed by NM, 27-Jun-1994.) |
Ref | Expression |
---|---|
nnon |
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | omelon 4423 |
. 2
![]() ![]() ![]() ![]() | |
2 | 1 | oneli 4255 |
1
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
Colors of variables: wff set class |
Syntax hints: ![]() ![]() ![]() ![]() |
This theorem was proved from axioms: ax-1 5 ax-2 6 ax-mp 7 ax-ia1 104 ax-ia2 105 ax-ia3 106 ax-in1 579 ax-in2 580 ax-io 665 ax-5 1381 ax-7 1382 ax-gen 1383 ax-ie1 1427 ax-ie2 1428 ax-8 1440 ax-10 1441 ax-11 1442 ax-i12 1443 ax-bndl 1444 ax-4 1445 ax-13 1449 ax-14 1450 ax-17 1464 ax-i9 1468 ax-ial 1472 ax-i5r 1473 ax-ext 2070 ax-sep 3957 ax-nul 3965 ax-pow 4009 ax-pr 4036 ax-un 4260 ax-iinf 4403 |
This theorem depends on definitions: df-bi 115 df-3an 926 df-tru 1292 df-nf 1395 df-sb 1693 df-clab 2075 df-cleq 2081 df-clel 2084 df-nfc 2217 df-ral 2364 df-rex 2365 df-v 2621 df-dif 3001 df-un 3003 df-in 3005 df-ss 3012 df-nul 3287 df-pw 3431 df-sn 3452 df-pr 3453 df-uni 3654 df-int 3689 df-tr 3937 df-iord 4193 df-on 4195 df-suc 4198 df-iom 4406 |
This theorem is referenced by: nnoni 4425 nnord 4426 omsson 4427 frecrdg 6173 onasuc 6227 onmsuc 6234 nna0 6235 nnm0 6236 nnasuc 6237 nnmsuc 6238 nnsucelsuc 6252 nnsucsssuc 6253 nntri2or2 6259 nnaordi 6265 nnaword1 6270 nnaordex 6284 phpelm 6580 phplem4on 6581 finnum 6809 pion 6867 prarloclemlo 7051 nnpredcl 11845 nnsucpred 11846 |
Copyright terms: Public domain | W3C validator |