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 φA
pncand.2 φB
Assertion negsubd φA+B=AB

Proof

Step Hyp Ref Expression
1 negidd.1 φA
2 pncand.2 φB
3 negsub ABA+B=AB
4 1 2 3 syl2anc φA+B=AB