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Mirrors > Home > ILE Home > Th. List > ltrelre | Unicode version |
Description: 'Less than' is a relation on real numbers. (Contributed by NM, 22-Feb-1996.) |
Ref | Expression |
---|---|
ltrelre |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | df-lt 7626 | . 2 | |
2 | opabssxp 4608 | . 2 | |
3 | 1, 2 | eqsstri 3124 | 1 |
Colors of variables: wff set class |
Syntax hints: wa 103 wceq 1331 wex 1468 wcel 1480 wss 3066 cop 3525 class class class wbr 3924 copab 3983 cxp 4532 c0r 7099 cltr 7104 cr 7612 cltrr 7617 |
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-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 2119 |
This theorem depends on definitions: df-bi 116 df-nf 1437 df-sb 1736 df-clab 2124 df-cleq 2130 df-clel 2133 df-nfc 2268 df-in 3072 df-ss 3079 df-opab 3985 df-xp 4540 df-lt 7626 |
This theorem is referenced by: ltresr 7640 |
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