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Mirrors > Home > MPE Home > Th. List > dvdszrcl | Unicode version |
Description: Reverse closure for the divisibility relation. (Contributed by Stefan O'Rear, 5-Sep-2015.) |
Ref | Expression |
---|---|
dvdszrcl |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | df-dvds 12808 |
. . 3
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2 | opabssxp 4909 |
. . 3
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3 | 1, 2 | eqsstri 3338 |
. 2
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4 | 3 | brel 4885 |
1
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Colors of variables: wff set class |
Syntax hints: ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
This theorem is referenced by: dvdsmulgcd 13009 oddvdsi 15141 odmulg 15147 gexdvdsi 15172 |
This theorem was proved from axioms: ax-1 5 ax-2 6 ax-3 7 ax-mp 8 ax-gen 1552 ax-5 1563 ax-17 1623 ax-9 1662 ax-8 1683 ax-14 1725 ax-6 1740 ax-7 1745 ax-11 1757 ax-12 1946 ax-ext 2385 ax-sep 4290 ax-nul 4298 ax-pr 4363 |
This theorem depends on definitions: df-bi 178 df-or 360 df-an 361 df-3an 938 df-tru 1325 df-ex 1548 df-nf 1551 df-sb 1656 df-clab 2391 df-cleq 2397 df-clel 2400 df-nfc 2529 df-ne 2569 df-ral 2671 df-rex 2672 df-rab 2675 df-v 2918 df-dif 3283 df-un 3285 df-in 3287 df-ss 3294 df-nul 3589 df-if 3700 df-sn 3780 df-pr 3781 df-op 3783 df-br 4173 df-opab 4227 df-xp 4843 df-dvds 12808 |
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