Theorem cjmulge0i

Description: A complex number times its conjugate is nonnegative. (Contributed by NM, 28-May-1999)

	Ref	Expression
Hypothesis	recl.1	⊢ 𝐴 ∈ ℂ
Assertion	cjmulge0i	⊢ 0 ≤ ( 𝐴 · ( ∗ ‘ 𝐴 ) )

Proof

Step	Hyp	Ref	Expression
1		recl.1	⊢ 𝐴 ∈ ℂ
2		cjmulge0	⊢ ( 𝐴 ∈ ℂ → 0 ≤ ( 𝐴 · ( ∗ ‘ 𝐴 ) ) )
3	1 2	ax-mp	⊢ 0 ≤ ( 𝐴 · ( ∗ ‘ 𝐴 ) )