Metamath Proof Explorer


Theorem recli

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

Proof

Step Hyp Ref Expression
1 recl.1 𝐴 ∈ ℂ
2 recl ( 𝐴 ∈ ℂ → ( ℜ ‘ 𝐴 ) ∈ ℝ )
3 1 2 ax-mp ( ℜ ‘ 𝐴 ) ∈ ℝ