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Metamath Proof Explorer

Theorem recjd

Description: Real part of a complex conjugate. (Contributed by Mario Carneiro, 29-May-2016)

		Ref	Expression
	Hypothesis	recld.1	$⊢ φ \to A \in ℂ$
	Assertion	recjd	$⊢ φ \to ℜ (\overline{A}) = ℜ (A)$

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