Theorem 0lt1o 6526

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 2205	. 2 |- (/) = (/)
2		el1o 6523	. 2 |- ( (/) e. 1o <-> (/) = (/) )
3	1, 2	mpbir 146	1 |- (/) e. 1o

Syntax hints:   = wceq 1373   e. wcel 2176   (/)c0 3460   1oc1o 6495

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 1470  ax-7 1471  ax-gen 1472  ax-ie1 1516  ax-ie2 1517  ax-8 1527  ax-10 1528  ax-11 1529  ax-i12 1530  ax-bndl 1532  ax-4 1533  ax-17 1549  ax-i9 1553  ax-ial 1557  ax-i5r 1558  ax-ext 2187  ax-nul 4170

This theorem depends on definitions:  df-bi 117  df-tru 1376  df-nf 1484  df-sb 1786  df-clab 2192  df-cleq 2198  df-clel 2201  df-nfc 2337  df-v 2774  df-dif 3168  df-un 3170  df-nul 3461  df-sn 3639  df-suc 4418  df-1o 6502

This theorem is referenced by:  nnaordex  6614  1domsn  6914  snexxph  7052  difinfsnlem  7201  difinfsn  7202  0ct  7209  ctmlemr  7210  ctssdclemn0  7212  exmidfodomrlemr  7310  exmidfodomrlemrALT  7311  1lt2pi  7453  archnqq  7530  prarloclemarch2  7532  pwle2  15935