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Mirrors > Home > ILE Home > Th. List > mul4 | Unicode version |
Description: Rearrangement of 4 factors. (Contributed by NM, 8-Oct-1999.) |
Ref | Expression |
---|---|
mul4 |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | mul32 7675 |
. . . . 5
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2 | 1 | oveq1d 5683 |
. . . 4
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3 | 2 | 3expa 1144 |
. . 3
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4 | 3 | adantrr 464 |
. 2
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5 | mulcl 7532 |
. . 3
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6 | mulass 7536 |
. . . 4
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7 | 6 | 3expb 1145 |
. . 3
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8 | 5, 7 | sylan 278 |
. 2
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9 | mulcl 7532 |
. . . 4
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10 | mulass 7536 |
. . . . 5
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11 | 10 | 3expb 1145 |
. . . 4
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12 | 9, 11 | sylan 278 |
. . 3
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13 | 12 | an4s 556 |
. 2
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14 | 4, 8, 13 | 3eqtr3d 2129 |
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 666 ax-5 1382 ax-7 1383 ax-gen 1384 ax-ie1 1428 ax-ie2 1429 ax-8 1441 ax-10 1442 ax-11 1443 ax-i12 1444 ax-bndl 1445 ax-4 1446 ax-17 1465 ax-i9 1469 ax-ial 1473 ax-i5r 1474 ax-ext 2071 ax-mulcl 7506 ax-mulcom 7509 ax-mulass 7511 |
This theorem depends on definitions: df-bi 116 df-3an 927 df-tru 1293 df-nf 1396 df-sb 1694 df-clab 2076 df-cleq 2082 df-clel 2085 df-nfc 2218 df-rex 2366 df-v 2624 df-un 3006 df-sn 3458 df-pr 3459 df-op 3461 df-uni 3662 df-br 3854 df-iota 4995 df-fv 5038 df-ov 5671 |
This theorem is referenced by: mul4i 7693 mul4d 7700 recextlem1 8183 divmuldivap 8242 mulexp 10057 demoivreALT 11126 |
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