Metamath Proof Explorer


Theorem 0red

Description: The number 0 is real, deduction form. (Contributed by David A. Wheeler, 6-Dec-2018)

Ref Expression
Assertion 0red ⊢ φ → 0 ∈ ℝ

Proof

Step Hyp Ref Expression
1 0re ⊢ 0 ∈ ℝ
2 1 a1i ⊢ φ → 0 ∈ ℝ