ILE Home Intuitionistic Logic Explorer < Previous   Next >
Nearby theorems
Mirrors  >  Home  >  ILE Home  >  Th. List  >  onn0 Unicode version

Theorem onn0 4137
Description: The class of all ordinal numbers is not empty. (Contributed by NM, 17-Sep-1995.)
Assertion
Ref Expression
onn0  |-  On  =/=  (/)

Proof of Theorem onn0
StepHypRef Expression
1 0elon 4129 . 2  |-  (/)  e.  On
2 ne0i 3230 . 2  |-  ( (/)  e.  On  ->  On  =/=  (/) )
31, 2ax-mp 7 1  |-  On  =/=  (/)
Colors of variables: wff set class
Syntax hints:    e. wcel 1393    =/= wne 2204   (/)c0 3224   Oncon0 4100
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 99  ax-ia2 100  ax-ia3 101  ax-in1 544  ax-in2 545  ax-io 630  ax-5 1336  ax-7 1337  ax-gen 1338  ax-ie1 1382  ax-ie2 1383  ax-8 1395  ax-10 1396  ax-11 1397  ax-i12 1398  ax-bndl 1399  ax-4 1400  ax-17 1419  ax-i9 1423  ax-ial 1427  ax-i5r 1428  ax-ext 2022  ax-nul 3883
This theorem depends on definitions:  df-bi 110  df-tru 1246  df-nf 1350  df-sb 1646  df-clab 2027  df-cleq 2033  df-clel 2036  df-nfc 2167  df-ne 2206  df-ral 2311  df-rex 2312  df-v 2559  df-dif 2920  df-in 2924  df-ss 2931  df-nul 3225  df-pw 3361  df-uni 3581  df-tr 3855  df-iord 4103  df-on 4105
This theorem is referenced by: (None)
  Copyright terms: Public domain W3C validator