Theorem 2on0 7151

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 7143	. 2 |- 2o = suc 1o
2		nsuceq0 4964	. 2 |- suc 1o =/= (/)
3	1, 2	eqnetri 2763	1 |- 2o =/= (/)

Syntax hints:   =/= wne 2662   (/)c0 3790   suc csuc 4886   1oc1o 7135   2oc2o 7136

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1601  ax-4 1612  ax-5 1680  ax-6 1719  ax-7 1739  ax-10 1786  ax-11 1791  ax-12 1803  ax-13 1968  ax-ext 2445  ax-nul 4582

This theorem depends on definitions:  df-bi 185  df-or 370  df-an 371  df-tru 1382  df-ex 1597  df-nf 1600  df-sb 1712  df-clab 2453  df-cleq 2459  df-clel 2462  df-nfc 2617  df-ne 2664  df-v 3120  df-dif 3484  df-un 3486  df-nul 3791  df-sn 4034  df-suc 4890  df-2o 7143

This theorem is referenced by:  snnen2o  7718  pmtrfmvdn0  16360  pmtrsn  16417  efgrcl  16606  sltval2  29343  sltintdifex  29350  onint1  29841  frlmpwfi  30974