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Mirrors > Home > MPE Home > Th. List > mulneg2d | Structured version Visualization version Unicode version |
Description: Product with negative is negative of product. (Contributed by Mario Carneiro, 27-May-2016.) |
Ref | Expression |
---|---|
mulm1d.1 |
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mulnegd.2 |
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Ref | Expression |
---|---|
mulneg2d |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | mulm1d.1 |
. 2
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2 | mulnegd.2 |
. 2
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3 | mulneg2 10056 |
. 2
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4 | 1, 2, 3 | syl2anc 667 |
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 1669 ax-4 1682 ax-5 1758 ax-6 1805 ax-7 1851 ax-8 1889 ax-9 1896 ax-10 1915 ax-11 1920 ax-12 1933 ax-13 2091 ax-ext 2431 ax-sep 4525 ax-nul 4534 ax-pow 4581 ax-pr 4639 ax-un 6583 ax-resscn 9596 ax-1cn 9597 ax-icn 9598 ax-addcl 9599 ax-addrcl 9600 ax-mulcl 9601 ax-mulrcl 9602 ax-mulcom 9603 ax-addass 9604 ax-mulass 9605 ax-distr 9606 ax-i2m1 9607 ax-1ne0 9608 ax-1rid 9609 ax-rnegex 9610 ax-rrecex 9611 ax-cnre 9612 ax-pre-lttri 9613 ax-pre-lttrn 9614 ax-pre-ltadd 9615 |
This theorem depends on definitions: df-bi 189 df-or 372 df-an 373 df-3or 986 df-3an 987 df-tru 1447 df-ex 1664 df-nf 1668 df-sb 1798 df-eu 2303 df-mo 2304 df-clab 2438 df-cleq 2444 df-clel 2447 df-nfc 2581 df-ne 2624 df-nel 2625 df-ral 2742 df-rex 2743 df-reu 2744 df-rab 2746 df-v 3047 df-sbc 3268 df-csb 3364 df-dif 3407 df-un 3409 df-in 3411 df-ss 3418 df-nul 3732 df-if 3882 df-pw 3953 df-sn 3969 df-pr 3971 df-op 3975 df-uni 4199 df-br 4403 df-opab 4462 df-mpt 4463 df-id 4749 df-po 4755 df-so 4756 df-xp 4840 df-rel 4841 df-cnv 4842 df-co 4843 df-dm 4844 df-rn 4845 df-res 4846 df-ima 4847 df-iota 5546 df-fun 5584 df-fn 5585 df-f 5586 df-f1 5587 df-fo 5588 df-f1o 5589 df-fv 5590 df-riota 6252 df-ov 6293 df-oprab 6294 df-mpt2 6295 df-er 7363 df-en 7570 df-dom 7571 df-sdom 7572 df-pnf 9677 df-mnf 9678 df-ltxr 9680 df-sub 9862 df-neg 9863 |
This theorem is referenced by: prodge0 10452 expmulz 12318 discr 12409 sincossq 14230 oexpneg 14368 mulgass 16788 zringlpirlem3OLD 19055 zringlpirlem3 19057 pjthlem1 22391 dvfsum2 22986 vieta1 23265 advlogexp 23600 logccv 23608 cxpmul2z 23636 abscxpbnd 23693 isosctrlem3 23749 dcubic1lem 23769 mcubic 23773 amgmlem 23915 ftalem5 24001 ftalem5OLD 24003 pntrlog2bndlem2 24416 brbtwn2 24935 colinearalglem4 24939 gxmodid 26007 pjhthlem1 27044 fwddifnp1 30932 areacirclem1 32032 pellexlem6 35678 pell1234qrreccl 35700 pell14qrdich 35715 rmxyneg 35768 rmxm1 35782 cosknegpi 37744 itgsinexplem1 37830 dirkerper 37958 sqwvfoura 38092 etransclem46 38145 oexpnegALTV 38806 oexpnegnz 38807 2zrngagrp 39996 |
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