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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 |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | df-iltp 7447 |
. 2
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2 | opabssxp 4696 |
. 2
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3 | 1, 2 | eqsstri 3187 |
1
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Colors of variables: wff set class |
Syntax hints: ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
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-io 709 ax-5 1447 ax-7 1448 ax-gen 1449 ax-ie1 1493 ax-ie2 1494 ax-8 1504 ax-10 1505 ax-11 1506 ax-i12 1507 ax-bndl 1509 ax-4 1510 ax-17 1526 ax-i9 1530 ax-ial 1534 ax-i5r 1535 ax-ext 2159 |
This theorem depends on definitions: df-bi 117 df-nf 1461 df-sb 1763 df-clab 2164 df-cleq 2170 df-clel 2173 df-nfc 2308 df-in 3135 df-ss 3142 df-opab 4062 df-xp 4628 df-iltp 7447 |
This theorem is referenced by: ltprordil 7566 ltexprlemm 7577 ltexprlemopl 7578 ltexprlemlol 7579 ltexprlemopu 7580 ltexprlemupu 7581 ltexprlemdisj 7583 ltexprlemloc 7584 ltexprlemfl 7586 ltexprlemrl 7587 ltexprlemfu 7588 ltexprlemru 7589 ltexpri 7590 lteupri 7594 ltaprlem 7595 prplnqu 7597 caucvgprprlemk 7660 caucvgprprlemnkltj 7666 caucvgprprlemnkeqj 7667 caucvgprprlemnjltk 7668 caucvgprprlemnbj 7670 caucvgprprlemml 7671 caucvgprprlemlol 7675 caucvgprprlemupu 7677 suplocexprlemss 7692 suplocexprlemlub 7701 gt0srpr 7725 lttrsr 7739 ltposr 7740 archsr 7759 |
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