Theorem 2on0 6934

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 6926	. 2 |- 2o = suc 1o
2		nsuceq0 4804	. 2 |- suc 1o =/= (/)
3	1, 2	eqnetri 2630	1 |- 2o =/= (/)

Syntax hints:   =/= wne 2611   (/)c0 3642   suc csuc 4726   1oc1o 6918   2oc2o 6919

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1591  ax-4 1602  ax-5 1670  ax-6 1708  ax-7 1728  ax-10 1775  ax-11 1780  ax-12 1792  ax-13 1943  ax-ext 2423  ax-nul 4426

This theorem depends on definitions:  df-bi 185  df-or 370  df-an 371  df-tru 1372  df-ex 1587  df-nf 1590  df-sb 1701  df-clab 2430  df-cleq 2436  df-clel 2439  df-nfc 2573  df-ne 2613  df-v 2979  df-dif 3336  df-un 3338  df-nul 3643  df-sn 3883  df-suc 4730  df-2o 6926

This theorem is referenced by:  pmtrfmvdn0  15973  efgrcl  16217  sltval2  27802  sltintdifex  27809  onint1  28300  frlmpwfi  29458  snnen2o  30743  pmtrsn  30775