Theorem abscji

Description: The absolute value of a number and its conjugate are the same. Proposition 10-3.7(b) of Gleason p. 133. (Contributed by NM, 2-Oct-1999)

	Ref	Expression
Hypothesis	absvalsqi.1	|- A e. CC
Assertion	abscji	|- ( abs ` ( * ` A ) ) = ( abs ` A )

Proof

Step	Hyp	Ref	Expression
1		absvalsqi.1	|- A e. CC
2		abscj	|- ( A e. CC -> ( abs ` ( * ` A ) ) = ( abs ` A ) )
3	1 2	ax-mp	|- ( abs ` ( * ` A ) ) = ( abs ` A )