Metamath Proof Explorer


Theorem subsub2d

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

Ref Expression
Hypotheses negidd.1 φ A
pncand.2 φ B
subaddd.3 φ C
Assertion subsub2d φ A B C = A + C - B

Proof

Step Hyp Ref Expression
1 negidd.1 φ A
2 pncand.2 φ B
3 subaddd.3 φ C
4 subsub2 A B C A B C = A + C - B
5 1 2 3 4 syl3anc φ A B C = A + C - B