Metamath Proof Explorer


Theorem neg2sub

Description: Relationship between subtraction and negative. (Contributed by Paul Chapman, 8-Oct-2007)

Ref Expression
Assertion neg2sub AB-A-B=BA

Proof

Step Hyp Ref Expression
1 negcl AA
2 subneg AB-A-B=-A+B
3 1 2 sylan AB-A-B=-A+B
4 negsubdi ABAB=-A+B
5 negsubdi2 ABAB=BA
6 3 4 5 3eqtr2d AB-A-B=BA