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Mirrors > Home > ILE Home > Th. List > add42 | Unicode version |
Description: Rearrangement of 4 terms in a sum. (Contributed by NM, 12-May-2005.) |
Ref | Expression |
---|---|
add42 |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | add4 7916 | . 2 | |
2 | addcom 7892 | . . . 4 | |
3 | 2 | ad2ant2l 499 | . . 3 |
4 | 3 | oveq2d 5783 | . 2 |
5 | 1, 4 | eqtrd 2170 | 1 |
Colors of variables: wff set class |
Syntax hints: wi 4 wa 103 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: add42d 7925 |
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