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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 | |
addd.2 | |
addd.3 | |
add4d.4 |
Ref | Expression |
---|---|
add4d |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | addd.1 | . 2 | |
2 | addd.2 | . 2 | |
3 | addd.3 | . 2 | |
4 | add4d.4 | . 2 | |
5 | add4 7916 | . 2 | |
6 | 1, 2, 3, 4, 5 | syl22anc 1217 | 1 |
Colors of variables: wff set class |
Syntax hints: wi 4 wceq 1331 wcel 1480 (class class class)co 5767 cc 7611 caddc 7616 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-ia1 105 ax-ia2 106 ax-ia3 107 ax-io 698 ax-5 1423 ax-7 1424 ax-gen 1425 ax-ie1 1469 ax-ie2 1470 ax-8 1482 ax-10 1483 ax-11 1484 ax-i12 1485 ax-bndl 1486 ax-4 1487 ax-17 1506 ax-i9 1510 ax-ial 1514 ax-i5r 1515 ax-ext 2119 ax-addcl 7709 ax-addcom 7713 ax-addass 7715 |
This theorem depends on definitions: df-bi 116 df-3an 964 df-tru 1334 df-nf 1437 df-sb 1736 df-clab 2124 df-cleq 2130 df-clel 2133 df-nfc 2268 df-rex 2420 df-v 2683 df-un 3070 df-sn 3528 df-pr 3529 df-op 3531 df-uni 3732 df-br 3925 df-iota 5083 df-fv 5126 df-ov 5770 |
This theorem is referenced by: apadd1 8363 binom3 10402 readd 10634 imadd 10642 max0addsup 10984 bdtri 11004 efi4p 11413 |
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