Theorem 2on0 7158

Description: Ordinal two is not zero. (Contributed by Scott Fenton, 17-Jun-2011.)

Assertion

Ref	Expression
2on0

Proof of Theorem 2on0

Step	Hyp	Ref	Expression
1		df-2o 7150	. 2
2		nsuceq0 4963	. 2
3	1, 2	eqnetri 2753	1

Syntax hints:  =/=wne 2652  c0 3784  succsuc 4885  c1o 7142  c2o 7143

This theorem is referenced by:  snnen2o  7726  pmtrfmvdn0  16487  pmtrsn  16544  efgrcl  16733  sltval2  29416  sltintdifex  29423  onint1  29914  frlmpwfi  31046

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1618  ax-4 1631  ax-5 1704  ax-6 1747  ax-7 1790  ax-10 1837  ax-11 1842  ax-12 1854  ax-13 1999  ax-ext 2435  ax-nul 4581

This theorem depends on definitions:  df-bi 185  df-or 370  df-an 371  df-tru 1398  df-ex 1613  df-nf 1617  df-sb 1740  df-clab 2443  df-cleq 2449  df-clel 2452  df-nfc 2607  df-ne 2654  df-v 3111  df-dif 3478  df-un 3480  df-nul 3785  df-sn 4030  df-suc 4889  df-2o 7150