Theorem cjcjd

Description: The conjugate of the conjugate is the original complex number. Proposition 10-3.4(e) of Gleason p. 133. (Contributed by Mario Carneiro, 29-May-2016)

	Ref	Expression
Hypothesis	recld.1	$$⊢\phi \to A\in ℂ$$
Assertion	cjcjd	$$⊢\phi \to \overline{\stackrel{‾}{A}}=A$$

Proof

Step	Hyp	Ref	Expression
1		recld.1	$$⊢\phi \to A\in ℂ$$
2		cjcj	$$⊢A\in ℂ\to \overline{\stackrel{‾}{A}}=A$$
3	1 2	syl	$$⊢\phi \to \overline{\stackrel{‾}{A}}=A$$