Metamath Proof Explorer


Theorem add42d

Description: Rearrangement of 4 terms in a sum. (Contributed by Mario Carneiro, 27-May-2016)

Ref Expression
Hypotheses addd.1 φ A
addd.2 φ B
addd.3 φ C
add4d.4 φ D
Assertion add42d φ A + B + C + D = A + C + D + B

Proof

Step Hyp Ref Expression
1 addd.1 φ A
2 addd.2 φ B
3 addd.3 φ C
4 add4d.4 φ D
5 add42 A B C D A + B + C + D = A + C + D + B
6 1 2 3 4 5 syl22anc φ A + B + C + D = A + C + D + B