Database
REAL AND COMPLEX NUMBERS
Real and complex numbers - basic operations
Subtraction
negcld
Next ⟩
subidd
Metamath Proof Explorer
Ascii
Unicode
Theorem
negcld
Description:
Closure law for negative.
(Contributed by
Mario Carneiro
, 27-May-2016)
Ref
Expression
Hypothesis
negidd.1
⊢
φ
→
A
∈
ℂ
Assertion
negcld
⊢
φ
→
−
A
∈
ℂ
Proof
Step
Hyp
Ref
Expression
1
negidd.1
⊢
φ
→
A
∈
ℂ
2
negcl
⊢
A
∈
ℂ
→
−
A
∈
ℂ
3
1
2
syl
⊢
φ
→
−
A
∈
ℂ