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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 |
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negeqd |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | negeqd.1 |
. 2
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2 | negeq 8167 |
. 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 106 ax-ia2 107 ax-ia3 108 ax-io 710 ax-5 1457 ax-7 1458 ax-gen 1459 ax-ie1 1503 ax-ie2 1504 ax-8 1514 ax-10 1515 ax-11 1516 ax-i12 1517 ax-bndl 1519 ax-4 1520 ax-17 1536 ax-i9 1540 ax-ial 1544 ax-i5r 1545 ax-ext 2170 |
This theorem depends on definitions: df-bi 117 df-3an 981 df-tru 1366 df-nf 1471 df-sb 1773 df-clab 2175 df-cleq 2181 df-clel 2184 df-nfc 2320 df-rex 2473 df-v 2753 df-un 3147 df-sn 3612 df-pr 3613 df-op 3615 df-uni 3824 df-br 4018 df-iota 5192 df-fv 5238 df-ov 5893 df-neg 8148 |
This theorem is referenced by: negdi 8231 mulneg2 8370 mulm1 8374 eqord2 8458 mulreim 8578 apneg 8585 divnegap 8680 div2negap 8709 recgt0 8824 infrenegsupex 9611 supminfex 9614 mul2lt0rlt0 9776 ceilqval 10323 ceilid 10332 modqcyc2 10377 monoord2 10494 reneg 10894 imneg 10902 cjcj 10909 cjneg 10916 minmax 11255 minabs 11261 telfsumo2 11492 sinneg 11751 tannegap 11753 sincossq 11773 odd2np1 11895 oexpneg 11899 modgcd 12009 pcneg 12341 mulgval 13029 mulgneg 13045 ivthdec 14505 limcimolemlt 14516 dvrecap 14560 sinperlem 14612 efimpi 14623 ptolemy 14628 lgsneg1 14809 lgseisenlem1 14833 m1lgs 14835 ex-ceil 14861 |
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