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Theorem 1n0 6016
 Description: Ordinal one is not equal to ordinal zero. (Contributed by NM, 26-Dec-2004.)
Assertion
Ref Expression
1n0

Proof of Theorem 1n0
StepHypRef Expression
1 df1o2 6013 . 2
2 0ex 3884 . . 3
32snnz 3487 . 2
41, 3eqnetri 2228 1
 Colors of variables: wff set class Syntax hints:   wne 2204  c0 3224  csn 3375  c1o 5994 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-v 2559  df-dif 2920  df-un 2922  df-nul 3225  df-sn 3381  df-suc 4108  df-1o 6001 This theorem is referenced by:  xp01disj  6017  1pi  6413
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