Theorem absmuli

Description: Absolute value distributes over multiplication. Proposition 10-3.7(f) of Gleason p. 133. (Contributed by NM, 1-Oct-1999)

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

Proof

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