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Mirrors > Home > MPE Home > Th. List > negidd | Structured version Unicode version |
Description: Addition of a number and its negative. (Contributed by Mario Carneiro, 27-May-2016.) |
Ref | Expression |
---|---|
negidd.1 |
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Ref | Expression |
---|---|
negidd |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | negidd.1 |
. 2
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2 | negid 9771 |
. 2
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3 | 1, 2 | syl 16 |
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 1710 ax-7 1730 ax-8 1760 ax-9 1762 ax-10 1777 ax-11 1782 ax-12 1794 ax-13 1955 ax-ext 2432 ax-sep 4524 ax-nul 4532 ax-pow 4581 ax-pr 4642 ax-un 6485 ax-resscn 9454 ax-1cn 9455 ax-icn 9456 ax-addcl 9457 ax-addrcl 9458 ax-mulcl 9459 ax-mulrcl 9460 ax-mulcom 9461 ax-addass 9462 ax-mulass 9463 ax-distr 9464 ax-i2m1 9465 ax-1ne0 9466 ax-1rid 9467 ax-rnegex 9468 ax-rrecex 9469 ax-cnre 9470 ax-pre-lttri 9471 ax-pre-lttrn 9472 ax-pre-ltadd 9473 |
This theorem depends on definitions: df-bi 185 df-or 370 df-an 371 df-3or 966 df-3an 967 df-tru 1373 df-ex 1588 df-nf 1591 df-sb 1703 df-eu 2266 df-mo 2267 df-clab 2440 df-cleq 2446 df-clel 2449 df-nfc 2604 df-ne 2650 df-nel 2651 df-ral 2804 df-rex 2805 df-reu 2806 df-rab 2808 df-v 3080 df-sbc 3295 df-csb 3399 df-dif 3442 df-un 3444 df-in 3446 df-ss 3453 df-nul 3749 df-if 3903 df-pw 3973 df-sn 3989 df-pr 3991 df-op 3995 df-uni 4203 df-br 4404 df-opab 4462 df-mpt 4463 df-id 4747 df-po 4752 df-so 4753 df-xp 4957 df-rel 4958 df-cnv 4959 df-co 4960 df-dm 4961 df-rn 4962 df-res 4963 df-ima 4964 df-iota 5492 df-fun 5531 df-fn 5532 df-f 5533 df-f1 5534 df-fo 5535 df-f1o 5536 df-fv 5537 df-riota 6164 df-ov 6206 df-oprab 6207 df-mpt2 6208 df-er 7214 df-en 7424 df-dom 7425 df-sdom 7426 df-pnf 9535 df-mnf 9536 df-ltxr 9538 df-sub 9712 df-neg 9713 |
This theorem is referenced by: xnegid 11321 xpncan 11329 moddvds 13664 bitsres 13791 pcadd2 14074 zaddablx 16475 zringinvg 18048 ditgsplit 21479 dvferm2lem 21601 vieta1 21921 geolim3 21948 ulmshft 21998 cxpneg 22269 dcubic1lem 22381 signsply0 27119 lgamgulmlem1 27182 itgaddnclem2 28622 pellexlem6 29346 pellfund14 29410 stoweidlem13 29979 stirlinglem5 30044 altgsumbcALT 30921 |
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