Metamath Proof Explorer


Theorem nppcan3d

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

Ref Expression
Hypotheses negidd.1 φ A
pncand.2 φ B
subaddd.3 φ C
Assertion nppcan3d φ A B + C + B = A + C

Proof

Step Hyp Ref Expression
1 negidd.1 φ A
2 pncand.2 φ B
3 subaddd.3 φ C
4 nppcan3 A B C A B + C + B = A + C
5 1 2 3 4 syl3anc φ A B + C + B = A + C