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Metamath Proof Explorer

Theorem cjdivi

Description: Complex conjugate distributes over division. (Contributed by NM, 29-Apr-2005) (Revised by Mario Carneiro, 29-May-2016)

	Ref	Expression
Hypotheses	recl.1	$⊢ A \in ℂ$
	readdi.2	$⊢ B \in ℂ$
Assertion	cjdivi	$⊢ B \neq 0 \to \overline{\frac{A}{B}} = \frac{\overline{A}}{\overline{B}}$

Step	Hyp	Ref	Expression
1		recl.1	$⊢ A \in ℂ$
2		readdi.2	$⊢ B \in ℂ$
3		cjdiv	$⊢ (A \in ℂ \land B \in ℂ \land B \neq 0) \to \overline{\frac{A}{B}} = \frac{\overline{A}}{\overline{B}}$
4	1 2 3	mp3an12	$⊢ B \neq 0 \to \overline{\frac{A}{B}} = \frac{\overline{A}}{\overline{B}}$