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REAL AND COMPLEX NUMBERS
Derive the basic properties from the field axioms
Some deductions from the field axioms for complex numbers
recnd
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Theorem
recnd
Description:
Deduction from real number to complex number.
(Contributed by
NM
, 26-Oct-1999)
Ref
Expression
Hypothesis
recnd.1
⊢
φ
→
A
∈
ℝ
Assertion
recnd
⊢
φ
→
A
∈
ℂ
Proof
Step
Hyp
Ref
Expression
1
recnd.1
⊢
φ
→
A
∈
ℝ
2
recn
⊢
A
∈
ℝ
→
A
∈
ℂ
3
1
2
syl
⊢
φ
→
A
∈
ℂ