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	$$⊢A\in ℂ$$
Assertion	cjcji	$$⊢\overline{\stackrel{‾}{A}}=A$$

Proof

Step	Hyp	Ref	Expression
1		recl.1	$$⊢A\in ℂ$$
2		cjcj	$$⊢A\in ℂ\to \overline{\stackrel{‾}{A}}=A$$
3	1 2	ax-mp	$$⊢\overline{\stackrel{‾}{A}}=A$$