Theorem 0lt1o 4137

Description: Ordinal zero is less than ordinal one.

Assertion

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

Proof of Theorem 0lt1o

Step	Hyp	Ref	Expression
1		eqid 1473	. 2 |- (/) = (/)
2		el1o 4136	. 2 |- ((/) e. 1o <-> (/) = (/))
3	1, 2	mpbir 190	1 |- (/) e. 1o

Syntax hints:   = wceq 954   e. wcel 956  (/)c0 2276  1oc1o 4118

This theorem is referenced by:  oe1m 4169  oen0 4203  oeordi 4204  1lt2pi 5012  indpi 5014

This theorem was proved from axioms:  ax-1 4  ax-2 5  ax-3 6  ax-mp 7  ax-7 960  ax-gen 961  ax-8 962  ax-10 964  ax-11 965  ax-12 966  ax-14 968  ax-17 969  ax-4 971  ax-5o 973  ax-6o 976  ax-9o 1121  ax-10o 1138  ax-16 1208  ax-11o 1216  ax-ext 1457  ax-nul 2705

This theorem depends on definitions:  df-bi 147  df-or 224  df-an 225  df-ex 979  df-sb 1170  df-eu 1380  df-mo 1381  df-clab 1462  df-cleq 1467  df-clel 1470  df-ne 1584  df-v 1808  df-dif 2045  df-un 2046  df-nul 2277  df-sn 2408  df-pr 2409  df-suc 2949  df-1o 4123

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