Theorem 0lt1o 4163

Description: Ordinal zero is less than ordinal one.

Assertion

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

Proof of Theorem 0lt1o

Step	Hyp	Ref	Expression
1		eqid 1482	. 2 |- (/) = (/)
2		el1o 4162	. 2 |- ((/) e. 1o <-> (/) = (/))
3	1, 2	mpbir 190	1 |- (/) e. 1o

Syntax hints:   = wceq 960   e. wcel 962  (/)c0 2291  1oc1o 4144

This theorem is referenced by:  oe1m 4195  oen0 4229  oeordi 4230  1lt2pi 5052  indpi 5054

This theorem was proved from axioms:  ax-1 4  ax-2 5  ax-3 6  ax-mp 7  ax-7 966  ax-gen 967  ax-8 968  ax-10 970  ax-11 971  ax-12 972  ax-14 974  ax-17 975  ax-4 977  ax-5o 979  ax-6o 982  ax-9o 1127  ax-10o 1144  ax-16 1214  ax-11o 1222  ax-ext 1464  ax-nul 2725

This theorem depends on definitions:  df-bi 147  df-or 224  df-an 225  df-ex 985  df-sb 1176  df-eu 1386  df-mo 1387  df-clab 1470  df-cleq 1475  df-clel 1478  df-ne 1594  df-v 1819  df-dif 2060  df-un 2061  df-nul 2292  df-sn 2424  df-pr 2425  df-suc 2970  df-1o 4149

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