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Mirrors > Home > ILE Home > Th. List > caucvgsrlemasr | Unicode version |
Description: Lemma for caucvgsr 7737. The lower bound is a signed real. (Contributed by Jim Kingdon, 4-Jul-2021.) |
Ref | Expression |
---|---|
caucvgsrlemasr.bnd |
Ref | Expression |
---|---|
caucvgsrlemasr |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | caucvgsrlemasr.bnd | . . 3 | |
2 | ltrelsr 7673 | . . . . . 6 | |
3 | 2 | brel 4653 | . . . . 5 |
4 | 3 | simpld 111 | . . . 4 |
5 | 4 | ralimi 2527 | . . 3 |
6 | 1, 5 | syl 14 | . 2 |
7 | 1pi 7250 | . . 3 | |
8 | elex2 2740 | . . 3 | |
9 | r19.3rmv 3497 | . . 3 | |
10 | 7, 8, 9 | mp2b 8 | . 2 |
11 | 6, 10 | sylibr 133 | 1 |
Colors of variables: wff set class |
Syntax hints: wi 4 wb 104 wex 1479 wcel 2135 wral 2442 class class class wbr 3979 cfv 5185 c1o 6371 cnpi 7207 cnr 7232 cltr 7238 |
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-in1 604 ax-in2 605 ax-io 699 ax-5 1434 ax-7 1435 ax-gen 1436 ax-ie1 1480 ax-ie2 1481 ax-8 1491 ax-10 1492 ax-11 1493 ax-i12 1494 ax-bndl 1496 ax-4 1497 ax-17 1513 ax-i9 1517 ax-ial 1521 ax-i5r 1522 ax-13 2137 ax-14 2138 ax-ext 2146 ax-sep 4097 ax-nul 4105 ax-pow 4150 ax-pr 4184 ax-un 4408 |
This theorem depends on definitions: df-bi 116 df-3an 969 df-tru 1345 df-nf 1448 df-sb 1750 df-clab 2151 df-cleq 2157 df-clel 2160 df-nfc 2295 df-ne 2335 df-ral 2447 df-rex 2448 df-v 2726 df-dif 3116 df-un 3118 df-in 3120 df-ss 3127 df-nul 3408 df-pw 3558 df-sn 3579 df-pr 3580 df-op 3582 df-uni 3787 df-int 3822 df-br 3980 df-opab 4041 df-suc 4346 df-iom 4565 df-xp 4607 df-1o 6378 df-ni 7239 df-ltr 7665 |
This theorem is referenced by: caucvgsrlemoffval 7731 caucvgsrlemofff 7732 caucvgsrlemoffcau 7733 caucvgsrlemoffgt1 7734 caucvgsrlemoffres 7735 |
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