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Mirrors > Home > ILE Home > Th. List > ltrelpr | Unicode version |
Description: Positive real 'less than' is a relation on positive reals. (Contributed by NM, 14-Feb-1996.) |
Ref | Expression |
---|---|
ltrelpr |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | df-iltp 7246 | . 2 | |
2 | opabssxp 4583 | . 2 | |
3 | 1, 2 | eqsstri 3099 | 1 |
Colors of variables: wff set class |
Syntax hints: wa 103 wcel 1465 wrex 2394 wss 3041 copab 3958 cxp 4507 cfv 5093 c1st 6004 c2nd 6005 cnq 7056 cnp 7067 cltp 7071 |
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 683 ax-5 1408 ax-7 1409 ax-gen 1410 ax-ie1 1454 ax-ie2 1455 ax-8 1467 ax-10 1468 ax-11 1469 ax-i12 1470 ax-bndl 1471 ax-4 1472 ax-17 1491 ax-i9 1495 ax-ial 1499 ax-i5r 1500 ax-ext 2099 |
This theorem depends on definitions: df-bi 116 df-nf 1422 df-sb 1721 df-clab 2104 df-cleq 2110 df-clel 2113 df-nfc 2247 df-in 3047 df-ss 3054 df-opab 3960 df-xp 4515 df-iltp 7246 |
This theorem is referenced by: ltprordil 7365 ltexprlemm 7376 ltexprlemopl 7377 ltexprlemlol 7378 ltexprlemopu 7379 ltexprlemupu 7380 ltexprlemdisj 7382 ltexprlemloc 7383 ltexprlemfl 7385 ltexprlemrl 7386 ltexprlemfu 7387 ltexprlemru 7388 ltexpri 7389 lteupri 7393 ltaprlem 7394 prplnqu 7396 caucvgprprlemk 7459 caucvgprprlemnkltj 7465 caucvgprprlemnkeqj 7466 caucvgprprlemnjltk 7467 caucvgprprlemnbj 7469 caucvgprprlemml 7470 caucvgprprlemlol 7474 caucvgprprlemupu 7476 suplocexprlemss 7491 suplocexprlemlub 7500 gt0srpr 7524 lttrsr 7538 ltposr 7539 archsr 7558 |
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