Theorem 2on0 7569

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 7561	. 2 |- 2o = suc 1o
2		nsuceq0 5805	. 2 |- suc 1o =/= (/)
3	1, 2	eqnetri 2864	1 |- 2o =/= (/)

Syntax hints:   =/= wne 2794   (/)c0 3915   suc csuc 5725   1oc1o 7553   2oc2o 7554

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1722  ax-4 1737  ax-5 1839  ax-6 1888  ax-7 1935  ax-9 1999  ax-10 2019  ax-11 2034  ax-12 2047  ax-13 2246  ax-ext 2602  ax-nul 4789

This theorem depends on definitions:  df-bi 197  df-or 385  df-an 386  df-tru 1486  df-ex 1705  df-nf 1710  df-sb 1881  df-clab 2609  df-cleq 2615  df-clel 2618  df-nfc 2753  df-ne 2795  df-v 3202  df-dif 3577  df-un 3579  df-nul 3916  df-sn 4178  df-suc 5729  df-2o 7561

This theorem is referenced by:  snnen2o  8149  pmtrfmvdn0  17882  pmtrsn  17939  efgrcl  18128  sltval2  31809  sltintdifex  31814  onint1  32448  1oequni2o  33216  finxpreclem4  33231  finxp3o  33237  frlmpwfi  37668  clsk1indlem1  38343