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Mirrors > Home > ILE Home > Th. List > add42d | 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 |
---|---|
add42d |
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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 | add42 8181 |
. 2
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6 | 1, 2, 3, 4, 5 | syl22anc 1250 |
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 710 ax-5 1458 ax-7 1459 ax-gen 1460 ax-ie1 1504 ax-ie2 1505 ax-8 1515 ax-10 1516 ax-11 1517 ax-i12 1518 ax-bndl 1520 ax-4 1521 ax-17 1537 ax-i9 1541 ax-ial 1545 ax-i5r 1546 ax-ext 2175 ax-addcl 7968 ax-addcom 7972 ax-addass 7974 |
This theorem depends on definitions: df-bi 117 df-3an 982 df-tru 1367 df-nf 1472 df-sb 1774 df-clab 2180 df-cleq 2186 df-clel 2189 df-nfc 2325 df-rex 2478 df-v 2762 df-un 3157 df-sn 3624 df-pr 3625 df-op 3627 df-uni 3836 df-br 4030 df-iota 5215 df-fv 5262 df-ov 5921 |
This theorem is referenced by: remullem 11015 mul4sqlem 12531 |
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