Metamath Proof Explorer

Theorem negsubd

Description: Relationship between subtraction and negative. Theorem I.3 of Apostol p. 18. (Contributed by Mario Carneiro, 27-May-2016)

Ref Expression
Hypotheses negidd.1 φ A
pncand.2 φ B
Assertion negsubd φ A + B = A B


Step Hyp Ref Expression
1 negidd.1 φ A
2 pncand.2 φ B
3 negsub A B A + B = A B
4 1 2 3 syl2anc φ A + B = A B