Metamath Proof Explorer


Theorem re0

Description: The real part of zero. (Contributed by NM, 27-Jul-1999)

Ref Expression
Assertion re0 ( ℜ ‘ 0 ) = 0

Proof

Step Hyp Ref Expression
1 0re 0 ∈ ℝ
2 rere ( 0 ∈ ℝ → ( ℜ ‘ 0 ) = 0 )
3 1 2 ax-mp ( ℜ ‘ 0 ) = 0