Theorem 0lt1o 6549

Description: Ordinal zero is less than ordinal one. (Contributed by NM, 5-Jan-2005.)

Assertion

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

Proof of Theorem 0lt1o

Step	Hyp	Ref	Expression
1		eqid 2207	. 2 |- (/) = (/)
2		el1o 6546	. 2 |- ( (/) e. 1o <-> (/) = (/) )
3	1, 2	mpbir 146	1 |- (/) e. 1o

Syntax hints:   = wceq 1373   e. wcel 2178   (/)c0 3468   1oc1o 6518

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 106  ax-ia2 107  ax-ia3 108  ax-in1 615  ax-in2 616  ax-io 711  ax-5 1471  ax-7 1472  ax-gen 1473  ax-ie1 1517  ax-ie2 1518  ax-8 1528  ax-10 1529  ax-11 1530  ax-i12 1531  ax-bndl 1533  ax-4 1534  ax-17 1550  ax-i9 1554  ax-ial 1558  ax-i5r 1559  ax-ext 2189  ax-nul 4186

This theorem depends on definitions:  df-bi 117  df-tru 1376  df-nf 1485  df-sb 1787  df-clab 2194  df-cleq 2200  df-clel 2203  df-nfc 2339  df-v 2778  df-dif 3176  df-un 3178  df-nul 3469  df-sn 3649  df-suc 4436  df-1o 6525

This theorem is referenced by:  nnaordex  6637  1domsn  6939  snexxph  7078  difinfsnlem  7227  difinfsn  7228  0ct  7235  ctmlemr  7236  ctssdclemn0  7238  exmidfodomrlemr  7341  exmidfodomrlemrALT  7342  iftrueb01  7369  1lt2pi  7488  archnqq  7565  prarloclemarch2  7567  dom1o  16128  pwle2  16137