Theorem recji

Description: Real part of a complex conjugate. (Contributed by NM, 2-Oct-1999)

	Ref	Expression
Hypothesis	recl.1	⊢ 𝐴 ∈ ℂ
Assertion	recji	⊢ ( ℜ ‘ ( ∗ ‘ 𝐴 ) ) = ( ℜ ‘ 𝐴 )

Proof

Step	Hyp	Ref	Expression
1		recl.1	⊢ 𝐴 ∈ ℂ
2		recj	⊢ ( 𝐴 ∈ ℂ → ( ℜ ‘ ( ∗ ‘ 𝐴 ) ) = ( ℜ ‘ 𝐴 ) )
3	1 2	ax-mp	⊢ ( ℜ ‘ ( ∗ ‘ 𝐴 ) ) = ( ℜ ‘ 𝐴 )