Theorem abssubi

Description: Swapping order of subtraction doesn't change the absolute value. Example of Apostol p. 363. (Contributed by NM, 1-Oct-1999)

	Ref	Expression
Hypotheses	absvalsqi.1	|- A e. CC
	abssub.2	|- B e. CC
Assertion	abssubi	|- ( abs ` ( A - B ) ) = ( abs ` ( B - A ) )

Proof

Step	Hyp	Ref	Expression
1		absvalsqi.1	|- A e. CC
2		abssub.2	|- B e. CC
3		abssub	|- ( ( A e. CC /\ B e. CC ) -> ( abs ` ( A - B ) ) = ( abs ` ( B - A ) ) )
4	1 2 3	mp2an	|- ( abs ` ( A - B ) ) = ( abs ` ( B - A ) )