Theorem 2on0 7057

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 7049	. 2 |- 2o = suc 1o
2		nsuceq0 4872	. 2 |- suc 1o =/= (/)
3	1, 2	eqnetri 2678	1 |- 2o =/= (/)

Syntax hints:   =/= wne 2577   (/)c0 3711   suc csuc 4794   1oc1o 7041   2oc2o 7042

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1626  ax-4 1639  ax-5 1712  ax-6 1755  ax-7 1798  ax-10 1845  ax-11 1850  ax-12 1862  ax-13 2006  ax-ext 2360  ax-nul 4496

This theorem depends on definitions:  df-bi 185  df-or 368  df-an 369  df-tru 1402  df-ex 1621  df-nf 1625  df-sb 1748  df-clab 2368  df-cleq 2374  df-clel 2377  df-nfc 2532  df-ne 2579  df-v 3036  df-dif 3392  df-un 3394  df-nul 3712  df-sn 3945  df-suc 4798  df-2o 7049

This theorem is referenced by:  snnen2o  7625  pmtrfmvdn0  16604  pmtrsn  16661  efgrcl  16850  sltval2  29581  sltintdifex  29588  onint1  30067  frlmpwfi  31214