Description: The real part of a complex number is real (closure law). (Contributed by NM, 11-May-1999)
Ref | Expression | ||
---|---|---|---|
Hypothesis | recl.1 | ⊢ 𝐴 ∈ ℂ | |
Assertion | recli | ⊢ ( ℜ ‘ 𝐴 ) ∈ ℝ |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | recl.1 | ⊢ 𝐴 ∈ ℂ | |
2 | recl | ⊢ ( 𝐴 ∈ ℂ → ( ℜ ‘ 𝐴 ) ∈ ℝ ) | |
3 | 1 2 | ax-mp | ⊢ ( ℜ ‘ 𝐴 ) ∈ ℝ |