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Mirrors > Home > ILE Home > Th. List > add4d | Unicode version |
Description: Rearrangement of 4 terms in a sum. (Contributed by Mario Carneiro, 27-May-2016.) |
Ref | Expression |
---|---|
addd.1 |
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addd.2 |
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addd.3 |
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add4d.4 |
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Ref | Expression |
---|---|
add4d |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | addd.1 |
. 2
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2 | addd.2 |
. 2
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3 | addd.3 |
. 2
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4 | add4d.4 |
. 2
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5 | add4 8116 |
. 2
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6 | 1, 2, 3, 4, 5 | syl22anc 1239 |
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 709 ax-5 1447 ax-7 1448 ax-gen 1449 ax-ie1 1493 ax-ie2 1494 ax-8 1504 ax-10 1505 ax-11 1506 ax-i12 1507 ax-bndl 1509 ax-4 1510 ax-17 1526 ax-i9 1530 ax-ial 1534 ax-i5r 1535 ax-ext 2159 ax-addcl 7906 ax-addcom 7910 ax-addass 7912 |
This theorem depends on definitions: df-bi 117 df-3an 980 df-tru 1356 df-nf 1461 df-sb 1763 df-clab 2164 df-cleq 2170 df-clel 2173 df-nfc 2308 df-rex 2461 df-v 2739 df-un 3133 df-sn 3598 df-pr 3599 df-op 3601 df-uni 3810 df-br 4004 df-iota 5178 df-fv 5224 df-ov 5877 |
This theorem is referenced by: apadd1 8563 binom3 10634 readd 10873 imadd 10881 max0addsup 11223 bdtri 11243 efi4p 11720 binom4 14290 |
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