Theorem 2on0 7188

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 7180	. 2 |- 2o = suc 1o
2		nsuceq0 5502	. 2 |- suc 1o =/= (/)
3	1, 2	eqnetri 2693	1 |- 2o =/= (/)

Syntax hints:   =/= wne 2621   (/)c0 3730   suc csuc 5424   1oc1o 7172   2oc2o 7173

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1668  ax-4 1681  ax-5 1757  ax-6 1804  ax-7 1850  ax-10 1914  ax-11 1919  ax-12 1932  ax-13 2090  ax-ext 2430  ax-nul 4533

This theorem depends on definitions:  df-bi 189  df-or 372  df-an 373  df-tru 1446  df-ex 1663  df-nf 1667  df-sb 1797  df-clab 2437  df-cleq 2443  df-clel 2446  df-nfc 2580  df-ne 2623  df-v 3046  df-dif 3406  df-un 3408  df-nul 3731  df-sn 3968  df-suc 5428  df-2o 7180

This theorem is referenced by:  snnen2o  7758  pmtrfmvdn0  17096  pmtrsn  17153  efgrcl  17358  sltval2  30536  sltintdifex  30543  onint1  31102  1oequni2o  31764  finxpreclem4  31779  finxp3o  31785  frlmpwfi  35950