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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 |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | add12 7791 |
. . . . 5
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2 | 1 | 3expb 1150 |
. . . 4
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3 | 2 | oveq2d 5722 |
. . 3
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4 | 3 | adantll 463 |
. 2
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5 | addcl 7617 |
. . 3
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6 | addass 7622 |
. . . 4
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7 | 6 | 3expa 1149 |
. . 3
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8 | 5, 7 | sylan2 282 |
. 2
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9 | addcl 7617 |
. . . 4
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10 | addass 7622 |
. . . . 5
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11 | 10 | 3expa 1149 |
. . . 4
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12 | 9, 11 | sylan2 282 |
. . 3
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13 | 12 | an4s 558 |
. 2
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14 | 4, 8, 13 | 3eqtr4d 2142 |
1
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Colors of variables: wff set class |
Syntax hints: ![]() ![]() ![]() ![]() ![]() ![]() |
This theorem was proved from axioms: ax-1 5 ax-2 6 ax-mp 7 ax-ia1 105 ax-ia2 106 ax-ia3 107 ax-io 671 ax-5 1391 ax-7 1392 ax-gen 1393 ax-ie1 1437 ax-ie2 1438 ax-8 1450 ax-10 1451 ax-11 1452 ax-i12 1453 ax-bndl 1454 ax-4 1455 ax-17 1474 ax-i9 1478 ax-ial 1482 ax-i5r 1483 ax-ext 2082 ax-addcl 7591 ax-addcom 7595 ax-addass 7597 |
This theorem depends on definitions: df-bi 116 df-3an 932 df-tru 1302 df-nf 1405 df-sb 1704 df-clab 2087 df-cleq 2093 df-clel 2096 df-nfc 2229 df-rex 2381 df-v 2643 df-un 3025 df-sn 3480 df-pr 3481 df-op 3483 df-uni 3684 df-br 3876 df-iota 5024 df-fv 5067 df-ov 5709 |
This theorem is referenced by: add42 7795 add4i 7798 add4d 7802 3dvds2dec 11358 opoe 11387 |
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