Theorem cjmuli

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

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

Proof

Step	Hyp	Ref	Expression
1		recl.1	$$⊢A\in ℂ$$
2		readdi.2	$$⊢B\in ℂ$$
3		cjmul	$$⊢\left(A\in ℂ\wedge B\in ℂ\right)\to \overline{AB}=\bar{A}\bar{B}$$
4	1 2 3	mp2an	$$⊢\overline{AB}=\bar{A}\bar{B}$$