Metamath Proof Explorer


Theorem 0reALT

Description: Alternate proof of 0re . (Contributed by NM, 19-Feb-2005) (Proof modification is discouraged.) (New usage is discouraged.)

Ref Expression
Assertion 0reALT ⊢ 0 ∈ ℝ

Proof

Step Hyp Ref Expression
1 ax-1cn ⊢ 1 ∈ ℂ
2 1 subidi ⊢ 1 − 1 = 0
3 1re ⊢ 1 ∈ ℝ
4 3 3 resubcli ⊢ 1 − 1 ∈ ℝ
5 2 4 eqeltrri ⊢ 0 ∈ ℝ