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 φA
addd.2 φB
addd.3 φC
add4d.4 φD
Assertion add42d φA+B+C+D=A+C+D+B

Proof

Step Hyp Ref Expression
1 addd.1 φA
2 addd.2 φB
3 addd.3 φC
4 add4d.4 φD
5 add42 ABCDA+B+C+D=A+C+D+B
6 1 2 3 4 5 syl22anc φA+B+C+D=A+C+D+B