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Mirrors > Home > ILE Home > Th. List > ltrelsr | Unicode version |
Description: Signed real 'less than' is a relation on signed reals. (Contributed by NM, 14-Feb-1996.) |
Ref | Expression |
---|---|
ltrelsr |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | df-ltr 7743 |
. 2
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2 | opabssxp 4712 |
. 2
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3 | 1, 2 | eqsstri 3199 |
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 710 ax-5 1457 ax-7 1458 ax-gen 1459 ax-ie1 1503 ax-ie2 1504 ax-8 1514 ax-10 1515 ax-11 1516 ax-i12 1517 ax-bndl 1519 ax-4 1520 ax-17 1536 ax-i9 1540 ax-ial 1544 ax-i5r 1545 ax-ext 2169 |
This theorem depends on definitions: df-bi 117 df-nf 1471 df-sb 1773 df-clab 2174 df-cleq 2180 df-clel 2183 df-nfc 2318 df-in 3147 df-ss 3154 df-opab 4077 df-xp 4644 df-ltr 7743 |
This theorem is referenced by: gt0srpr 7761 recexgt0sr 7786 addgt0sr 7788 mulgt0sr 7791 caucvgsrlemcl 7802 caucvgsrlemasr 7803 caucvgsrlemfv 7804 map2psrprg 7818 suplocsrlemb 7819 suplocsrlempr 7820 suplocsrlem 7821 suplocsr 7822 ltresr 7852 axpre-ltirr 7895 axpre-lttrn 7897 |
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