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Mirrors > Home > ILE Home > Th. List > caucvgsrlemasr | Unicode version |
Description: Lemma for caucvgsr 7815. The lower bound is a signed real. (Contributed by Jim Kingdon, 4-Jul-2021.) |
Ref | Expression |
---|---|
caucvgsrlemasr.bnd |
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Ref | Expression |
---|---|
caucvgsrlemasr |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | caucvgsrlemasr.bnd |
. . 3
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2 | ltrelsr 7751 |
. . . . . 6
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3 | 2 | brel 4690 |
. . . . 5
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4 | 3 | simpld 112 |
. . . 4
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5 | 4 | ralimi 2550 |
. . 3
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6 | 1, 5 | syl 14 |
. 2
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7 | 1pi 7328 |
. . 3
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8 | elex2 2765 |
. . 3
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9 | r19.3rmv 3525 |
. . 3
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10 | 7, 8, 9 | mp2b 8 |
. 2
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11 | 6, 10 | sylibr 134 |
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-in1 615 ax-in2 616 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-13 2160 ax-14 2161 ax-ext 2169 ax-sep 4133 ax-nul 4141 ax-pow 4186 ax-pr 4221 ax-un 4445 |
This theorem depends on definitions: df-bi 117 df-3an 981 df-tru 1366 df-nf 1471 df-sb 1773 df-clab 2174 df-cleq 2180 df-clel 2183 df-nfc 2318 df-ne 2358 df-ral 2470 df-rex 2471 df-v 2751 df-dif 3143 df-un 3145 df-in 3147 df-ss 3154 df-nul 3435 df-pw 3589 df-sn 3610 df-pr 3611 df-op 3613 df-uni 3822 df-int 3857 df-br 4016 df-opab 4077 df-suc 4383 df-iom 4602 df-xp 4644 df-1o 6431 df-ni 7317 df-ltr 7743 |
This theorem is referenced by: caucvgsrlemoffval 7809 caucvgsrlemofff 7810 caucvgsrlemoffcau 7811 caucvgsrlemoffgt1 7812 caucvgsrlemoffres 7813 |
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