Metamath Proof Explorer


Theorem zred

Description: An integer is a real number. (Contributed by Mario Carneiro, 28-May-2016)

Ref Expression
Hypothesis zred.1 ⊢ φ → A ∈ ℤ
Assertion zred ⊢ φ → A ∈ ℝ

Proof

Step Hyp Ref Expression
1 zred.1 ⊢ φ → A ∈ ℤ
2 zssre ⊢ ℤ ⊆ ℝ
3 2 1 sselid ⊢ φ → A ∈ ℝ