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Mirrors > Home > ILE Home > Th. List > negeqd | Unicode version |
Description: Equality deduction for negatives. (Contributed by NM, 14-May-1999.) |
Ref | Expression |
---|---|
negeqd.1 |
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Ref | Expression |
---|---|
negeqd |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | negeqd.1 |
. 2
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2 | negeq 7979 |
. 2
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3 | 1, 2 | syl 14 |
1
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Colors of variables: wff set class |
Syntax hints: ![]() ![]() ![]() |
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-io 699 ax-5 1424 ax-7 1425 ax-gen 1426 ax-ie1 1470 ax-ie2 1471 ax-8 1483 ax-10 1484 ax-11 1485 ax-i12 1486 ax-bndl 1487 ax-4 1488 ax-17 1507 ax-i9 1511 ax-ial 1515 ax-i5r 1516 ax-ext 2122 |
This theorem depends on definitions: df-bi 116 df-3an 965 df-tru 1335 df-nf 1438 df-sb 1737 df-clab 2127 df-cleq 2133 df-clel 2136 df-nfc 2271 df-rex 2423 df-v 2691 df-un 3080 df-sn 3538 df-pr 3539 df-op 3541 df-uni 3745 df-br 3938 df-iota 5096 df-fv 5139 df-ov 5785 df-neg 7960 |
This theorem is referenced by: negdi 8043 mulneg2 8182 mulm1 8186 eqord2 8270 mulreim 8390 apneg 8397 divnegap 8490 div2negap 8519 recgt0 8632 infrenegsupex 9416 supminfex 9419 mul2lt0rlt0 9576 ceilqval 10110 ceilid 10119 modqcyc2 10164 monoord2 10281 reneg 10672 imneg 10680 cjcj 10687 cjneg 10694 minmax 11033 minabs 11039 telfsumo2 11268 sinneg 11469 tannegap 11471 sincossq 11491 odd2np1 11606 oexpneg 11610 modgcd 11715 ivthdec 12830 limcimolemlt 12841 dvrecap 12885 sinperlem 12937 efimpi 12948 ptolemy 12953 ex-ceil 13109 |
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