Metamath Proof Explorer


Theorem addassd

Description: Associative law for addition. (Contributed by Mario Carneiro, 27-May-2016)

Ref Expression
Hypotheses addcld.1 φA
addcld.2 φB
addassd.3 φC
Assertion addassd φA+B+C=A+B+C

Proof

Step Hyp Ref Expression
1 addcld.1 φA
2 addcld.2 φB
3 addassd.3 φC
4 addass ABCA+B+C=A+B+C
5 1 2 3 4 syl3anc φA+B+C=A+B+C