Metamath Proof Explorer

Theorem abssubd

Description: Swapping order of subtraction doesn't change the absolute value. Example of Apostol p. 363. (Contributed by Mario Carneiro, 29-May-2016)

Ref Expression
Hypotheses abscld.1 φ A
abssubd.2 φ B
Assertion abssubd φ A B = B A


Step Hyp Ref Expression
1 abscld.1 φ A
2 abssubd.2 φ B
3 abssub A B A B = B A
4 1 2 3 syl2anc φ A B = B A