Metamath Proof Explorer


Theorem peano2re

Description: A theorem for reals analogous the second Peano postulate peano2nn . (Contributed by NM, 5-Jul-2005)

Ref Expression
Assertion peano2re ⊢ A ∈ ℝ → A + 1 ∈ ℝ

Proof

Step Hyp Ref Expression
1 1re ⊢ 1 ∈ ℝ
2 readdcl ⊢ A ∈ ℝ ∧ 1 ∈ ℝ → A + 1 ∈ ℝ
3 1 2 mpan2 ⊢ A ∈ ℝ → A + 1 ∈ ℝ