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Mirrors > Home > MPE Home > Th. List > grpodivval | Structured version Unicode version |
Description: Group division (or subtraction) operation value. (Contributed by NM, 15-Feb-2008.) (Revised by Mario Carneiro, 15-Dec-2013.) (New usage is discouraged.) |
Ref | Expression |
---|---|
grpdiv.1 |
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grpdiv.2 |
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grpdiv.3 |
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Ref | Expression |
---|---|
grpodivval |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | grpdiv.1 |
. . . . 5
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2 | grpdiv.2 |
. . . . 5
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3 | grpdiv.3 |
. . . . 5
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4 | 1, 2, 3 | grpodivfval 23850 |
. . . 4
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5 | 4 | oveqd 6193 |
. . 3
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6 | oveq1 6183 |
. . . 4
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7 | fveq2 5775 |
. . . . 5
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8 | 7 | oveq2d 6192 |
. . . 4
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9 | eqid 2450 |
. . . 4
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10 | ovex 6201 |
. . . 4
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11 | 6, 8, 9, 10 | ovmpt2 6312 |
. . 3
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12 | 5, 11 | sylan9eq 2510 |
. 2
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13 | 12 | 3impb 1184 |
1
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Colors of variables: wff setvar class |
Syntax hints: ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1592 ax-4 1603 ax-5 1671 ax-6 1709 ax-7 1729 ax-8 1759 ax-9 1761 ax-10 1776 ax-11 1781 ax-12 1793 ax-13 1944 ax-ext 2429 ax-rep 4487 ax-sep 4497 ax-nul 4505 ax-pow 4554 ax-pr 4615 ax-un 6458 |
This theorem depends on definitions: df-bi 185 df-or 370 df-an 371 df-3an 967 df-tru 1373 df-ex 1588 df-nf 1591 df-sb 1702 df-eu 2263 df-mo 2264 df-clab 2436 df-cleq 2442 df-clel 2445 df-nfc 2598 df-ne 2643 df-ral 2797 df-rex 2798 df-reu 2799 df-rab 2801 df-v 3056 df-sbc 3271 df-csb 3373 df-dif 3415 df-un 3417 df-in 3419 df-ss 3426 df-nul 3722 df-if 3876 df-pw 3946 df-sn 3962 df-pr 3964 df-op 3968 df-uni 4176 df-iun 4257 df-br 4377 df-opab 4435 df-mpt 4436 df-id 4720 df-xp 4930 df-rel 4931 df-cnv 4932 df-co 4933 df-dm 4934 df-rn 4935 df-res 4936 df-ima 4937 df-iota 5465 df-fun 5504 df-fn 5505 df-f 5506 df-f1 5507 df-fo 5508 df-f1o 5509 df-fv 5510 df-ov 6179 df-oprab 6180 df-mpt2 6181 df-1st 6663 df-2nd 6664 df-gdiv 23802 |
This theorem is referenced by: grpodivinv 23852 grpoinvdiv 23853 grpodivdiv 23856 grpomuldivass 23857 grpodivid 23858 grponpcan 23860 grpopnpcan2 23861 grponnncan2 23862 ablodivdiv4 23899 nvmval 24143 rngosub 28878 |
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