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 ∈ ℂ
Assertion	abscji	⊢ ( abs ‘ ( ∗ ‘ 𝐴 ) ) = ( abs ‘ 𝐴 )

Proof

Step	Hyp	Ref	Expression
1		absvalsqi.1	⊢ 𝐴 ∈ ℂ
2		abscj	⊢ ( 𝐴 ∈ ℂ → ( abs ‘ ( ∗ ‘ 𝐴 ) ) = ( abs ‘ 𝐴 ) )
3	1 2	ax-mp	⊢ ( abs ‘ ( ∗ ‘ 𝐴 ) ) = ( abs ‘ 𝐴 )