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Metamath Proof Explorer

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	$⊢ φ \to A \in ℂ$
	Assertion	cjcjd	$⊢ φ \to \overline{\overline{A}} = A$

Proof

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