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Mirrors > Home > ILE Home > Th. List > add4 | Unicode version |
Description: Rearrangement of 4 terms in a sum. (Contributed by NM, 13-Nov-1999.) (Proof shortened by Andrew Salmon, 22-Oct-2011.) |
Ref | Expression |
---|---|
add4 |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | add12 7266 | . . . . 5 | |
2 | 1 | 3expb 1139 | . . . 4 |
3 | 2 | oveq2d 5548 | . . 3 |
4 | 3 | adantll 459 | . 2 |
5 | addcl 7098 | . . 3 | |
6 | addass 7103 | . . . 4 | |
7 | 6 | 3expa 1138 | . . 3 |
8 | 5, 7 | sylan2 280 | . 2 |
9 | addcl 7098 | . . . 4 | |
10 | addass 7103 | . . . . 5 | |
11 | 10 | 3expa 1138 | . . . 4 |
12 | 9, 11 | sylan2 280 | . . 3 |
13 | 12 | an4s 552 | . 2 |
14 | 4, 8, 13 | 3eqtr4d 2123 | 1 |
Colors of variables: wff set class |
Syntax hints: wi 4 wa 102 wceq 1284 wcel 1433 (class class class)co 5532 cc 6979 caddc 6984 |
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 ax-addcl 7072 ax-addcom 7076 ax-addass 7078 |
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 |
This theorem is referenced by: add42 7270 add4i 7273 add4d 7277 3dvds2dec 10265 opoe 10295 |
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