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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 |
Ref | Expression |
---|---|
negeqd |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | negeqd.1 | . 2 | |
2 | negeq 7301 | . 2 | |
3 | 1, 2 | syl 14 | 1 |
Colors of variables: wff set class |
Syntax hints: wi 4 wceq 1284 cneg 7280 |
This theorem was proved from axioms: ax-1 5 ax-2 6 ax-mp 7 ax-ia1 104 ax-ia2 105 ax-ia3 106 ax-io 662 ax-5 1376 ax-7 1377 ax-gen 1378 ax-ie1 1422 ax-ie2 1423 ax-8 1435 ax-10 1436 ax-11 1437 ax-i12 1438 ax-bndl 1439 ax-4 1440 ax-17 1459 ax-i9 1463 ax-ial 1467 ax-i5r 1468 ax-ext 2063 |
This theorem depends on definitions: df-bi 115 df-3an 921 df-tru 1287 df-nf 1390 df-sb 1686 df-clab 2068 df-cleq 2074 df-clel 2077 df-nfc 2208 df-rex 2354 df-v 2603 df-un 2977 df-sn 3404 df-pr 3405 df-op 3407 df-uni 3602 df-br 3786 df-iota 4887 df-fv 4930 df-ov 5535 df-neg 7282 |
This theorem is referenced by: negdi 7365 mulneg2 7500 mulm1 7504 mulreim 7704 apneg 7711 divnegap 7794 div2negap 7823 recgt0 7928 infrenegsupex 8682 supminfex 8685 ceilqval 9308 ceilid 9317 modqcyc2 9362 monoord2 9456 reneg 9755 imneg 9763 cjcj 9770 cjneg 9777 minmax 10112 odd2np1 10272 oexpneg 10276 modgcd 10382 ex-ceil 10564 |
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