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Metamath Proof Explorer

Theorem cjaddi

Description: Complex conjugate distributes over addition. Proposition 10-3.4(a) of Gleason p. 133. (Contributed by NM, 28-Jul-1999)

	Ref	Expression
Hypotheses	recl.1	$⊢ A \in ℂ$
	readdi.2	$⊢ B \in ℂ$
Assertion	cjaddi	$⊢ \overline{A + B} = \overline{A} + \overline{B}$

Step	Hyp	Ref	Expression
1		recl.1	$⊢ A \in ℂ$
2		readdi.2	$⊢ B \in ℂ$
3		cjadd	$⊢ (A \in ℂ \land B \in ℂ) \to \overline{A + B} = \overline{A} + \overline{B}$
4	1 2 3	mp2an	$⊢ \overline{A + B} = \overline{A} + \overline{B}$