Metamath Proof Explorer


Theorem addsubassd

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

Ref Expression
Hypotheses negidd.1 φ A
pncand.2 φ B
subaddd.3 φ C
Assertion addsubassd φ A + B - C = A + B - C

Proof

Step Hyp Ref Expression
1 negidd.1 φ A
2 pncand.2 φ B
3 subaddd.3 φ C
4 addsubass A B C A + B - C = A + B - C
5 1 2 3 4 syl3anc φ A + B - C = A + B - C