Theorem 0lt1o 4147

Description: Ordinal zero is less than ordinal one.

Assertion

Ref	Expression
0lt1o	|- (/) e. 1o

Proof of Theorem 0lt1o

Step	Hyp	Ref	Expression
1		eqid 1475	. 2 |- (/) = (/)
2		el1o 4146	. 2 |- ((/) e. 1o <-> (/) = (/))
3	1, 2	mpbir 190	1 |- (/) e. 1o

Syntax hints:   = wceq 956   e. wcel 958  (/)c0 2280  1oc1o 4128

This theorem is referenced by:  oe1m 4179  oen0 4213  oeordi 4214  1lt2pi 5032  indpi 5034

This theorem was proved from axioms:  ax-1 4  ax-2 5  ax-3 6  ax-mp 7  ax-7 962  ax-gen 963  ax-8 964  ax-10 966  ax-11 967  ax-12 968  ax-14 970  ax-17 971  ax-4 973  ax-5o 975  ax-6o 978  ax-9o 1123  ax-10o 1140  ax-16 1210  ax-11o 1218  ax-ext 1459  ax-nul 2710

This theorem depends on definitions:  df-bi 147  df-or 224  df-an 225  df-ex 981  df-sb 1172  df-eu 1382  df-mo 1383  df-clab 1464  df-cleq 1469  df-clel 1472  df-ne 1587  df-v 1812  df-dif 2049  df-un 2050  df-nul 2281  df-sn 2412  df-pr 2413  df-suc 2954  df-1o 4133

Copyright terms: Public domain