Theorem cjcji

Description: The conjugate of the conjugate is the original complex number. Proposition 10-3.4(e) of Gleason p. 133. (Contributed by NM, 11-May-1999)

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

Proof

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