Theorem 2on0 8096

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

Assertion

Ref	Expression
2on0	⊢ 2o ≠ ∅

Proof of Theorem 2on0

Step	Hyp	Ref	Expression
1		df-2o 8086	. 2 ⊢ 2o = suc 1o
2		nsuceq0 6239	. 2 ⊢ suc 1o ≠ ∅
3	1, 2	eqnetri 3057	1 ⊢ 2o ≠ ∅

Syntax hints:   ≠ wne 2987  ∅c0 4243  suc csuc 6161  1_oc1o 8078  2_oc2o 8079

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1797  ax-4 1811  ax-5 1911  ax-6 1970  ax-7 2015  ax-8 2113  ax-9 2121  ax-ext 2770  ax-nul 5174

This theorem depends on definitions:  df-bi 210  df-an 400  df-or 845  df-ex 1782  df-sb 2070  df-clab 2777  df-cleq 2791  df-clel 2870  df-ne 2988  df-v 3443  df-dif 3884  df-un 3886  df-nul 4244  df-sn 4526  df-suc 6165  df-2o 8086

This theorem is referenced by:  snnen2o  8691  pmtrfmvdn0  18582  pmtrsn  18639  efgrcl  18833  goaln0  32753  goalr  32757  fmla0disjsuc  32758  sltval2  33276  sltintdifex  33281  onint1  33910  1oequni2o  34785  finxpreclem4  34811  finxp3o  34817  frlmpwfi  40042  clsk1indlem1  40748