Database
REAL AND COMPLEX NUMBERS
Elementary real and complex functions
Real and imaginary parts; conjugate
renegi
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imnegi
Metamath Proof Explorer
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Unicode
Theorem
renegi
Description:
Real part of negative.
(Contributed by
NM
, 2-Aug-1999)
Ref
Expression
Hypothesis
recl.1
⊢
A
∈
ℂ
Assertion
renegi
⊢
ℜ
⁡
−
A
=
−
ℜ
⁡
A
Proof
Step
Hyp
Ref
Expression
1
recl.1
⊢
A
∈
ℂ
2
reneg
⊢
A
∈
ℂ
→
ℜ
⁡
−
A
=
−
ℜ
⁡
A
3
1
2
ax-mp
⊢
ℜ
⁡
−
A
=
−
ℜ
⁡
A