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Mirrors > Home > ILE Home > Th. List > 0lt1o | Unicode version |
Description: Ordinal zero is less than ordinal one. (Contributed by NM, 5-Jan-2005.) |
Ref | Expression |
---|---|
0lt1o |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | eqid 2139 | . 2 | |
2 | el1o 6334 | . 2 | |
3 | 1, 2 | mpbir 145 | 1 |
Colors of variables: wff set class |
Syntax hints: wceq 1331 wcel 1480 c0 3363 c1o 6306 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-ia1 105 ax-ia2 106 ax-ia3 107 ax-in1 603 ax-in2 604 ax-io 698 ax-5 1423 ax-7 1424 ax-gen 1425 ax-ie1 1469 ax-ie2 1470 ax-8 1482 ax-10 1483 ax-11 1484 ax-i12 1485 ax-bndl 1486 ax-4 1487 ax-17 1506 ax-i9 1510 ax-ial 1514 ax-i5r 1515 ax-ext 2121 ax-nul 4054 |
This theorem depends on definitions: df-bi 116 df-tru 1334 df-nf 1437 df-sb 1736 df-clab 2126 df-cleq 2132 df-clel 2135 df-nfc 2270 df-v 2688 df-dif 3073 df-un 3075 df-nul 3364 df-sn 3533 df-suc 4293 df-1o 6313 |
This theorem is referenced by: nnaordex 6423 1domsn 6713 snexxph 6838 difinfsnlem 6984 difinfsn 6985 0ct 6992 ctmlemr 6993 ctssdclemn0 6995 exmidfodomrlemr 7058 exmidfodomrlemrALT 7059 1lt2pi 7148 archnqq 7225 prarloclemarch2 7227 pwle2 13193 |
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