Database
REAL AND COMPLEX NUMBERS
Elementary real and complex functions
Real and imaginary parts; conjugate
cjmulge0i
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Metamath Proof Explorer
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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
‾