Metamath Proof Explorer


Theorem pire

Description: _pi is a real number. (Contributed by Paul Chapman, 23-Jan-2008)

Ref Expression
Assertion pire ⊢ π ∈ ℝ

Proof

Step Hyp Ref Expression
1 pilem3 ⊢ π ∈ 2 4 ∧ sin ⁡ π = 0
2 1 simpli ⊢ π ∈ 2 4
3 elioore ⊢ π ∈ 2 4 → π ∈ ℝ
4 2 3 ax-mp ⊢ π ∈ ℝ