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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 6568 | . 2 | |
2 | opabssxp 4414 | . 2 | |
3 | 1, 2 | eqsstri 2975 | 1 |
Colors of variables: wff set class |
Syntax hints: wa 97 wcel 1393 wrex 2307 wss 2917 copab 3817 cxp 4343 cfv 4902 c1st 5765 c2nd 5766 cnq 6378 cnp 6389 cltp 6393 |
This theorem was proved from axioms: ax-1 5 ax-2 6 ax-mp 7 ax-ia1 99 ax-ia2 100 ax-ia3 101 ax-io 630 ax-5 1336 ax-7 1337 ax-gen 1338 ax-ie1 1382 ax-ie2 1383 ax-8 1395 ax-10 1396 ax-11 1397 ax-i12 1398 ax-bndl 1399 ax-4 1400 ax-17 1419 ax-i9 1423 ax-ial 1427 ax-i5r 1428 ax-ext 2022 |
This theorem depends on definitions: df-bi 110 df-nf 1350 df-sb 1646 df-clab 2027 df-cleq 2033 df-clel 2036 df-nfc 2167 df-in 2924 df-ss 2931 df-opab 3819 df-xp 4351 df-iltp 6568 |
This theorem is referenced by: ltprordil 6687 ltexprlemm 6698 ltexprlemopl 6699 ltexprlemlol 6700 ltexprlemopu 6701 ltexprlemupu 6702 ltexprlemdisj 6704 ltexprlemloc 6705 ltexprlemfl 6707 ltexprlemrl 6708 ltexprlemfu 6709 ltexprlemru 6710 ltexpri 6711 lteupri 6715 ltaprlem 6716 prplnqu 6718 caucvgprprlemk 6781 caucvgprprlemnkltj 6787 caucvgprprlemnkeqj 6788 caucvgprprlemnjltk 6789 caucvgprprlemnbj 6791 caucvgprprlemml 6792 caucvgprprlemlol 6796 caucvgprprlemupu 6798 gt0srpr 6833 lttrsr 6847 ltposr 6848 archsr 6866 |
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