Theorem 0ne1oOLD 3113

Description: Ordinal zero is not equal to ordinal one.

Assertion

Ref	Expression
0ne1oOLD	|- -. (/) = 1o

Proof of Theorem 0ne1oOLD

Step	Hyp	Ref	Expression
1		0nep0 1887	. 2 |- -. (/) = {(/)}
2		df1o2 3111	. . 3 |- 1o = {(/)}
3	2	cleq2i 1111	. 2 |- ((/) = 1o <-> (/) = {(/)})
4	1, 3	mtbir 167	1 |- -. (/) = 1o

Syntax hints:  -. wn 1   = wceq 1091  (/)c0 1707  {csn 1808  1oc1o 3099

This theorem is referenced by:  unxpdom2 3651  sucxpdom 3652  uncdadom 3718  cdaen 3719  cda1en 3721  cdacomen 3724  cdaassen 3725  xpcdaen 3726  cdadom1 3727

This theorem was proved from axioms:  ax-1 3  ax-2 4  ax-3 5  ax-mp 6  ax-4 673  ax-5 674  ax-6 675  ax-7 676  ax-gen 677  ax-8 798  ax-9 799  ax-10 800  ax-11 801  ax-12 802  ax-14 805  ax-16 922  ax-17 925  ax-ext 1074  ax-rep 1075

This theorem depends on definitions:  df-bi 128  df-or 197  df-an 198  df-ex 679  df-sb 853  df-clab 1093  df-cleq 1097  df-clel 1099  df-v 1349  df-dif 1489  df-un 1490  df-in 1491  df-nul 1708  df-sn 1811  df-pr 1812  df-suc 2205  df-1o 3104

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