Description: Real number version of addrid without ax-mulcom . (Contributed by SN, 23-Jan-2024)
Ref | Expression | ||
---|---|---|---|
Assertion | readdrid | ⊢ ( 𝐴 ∈ ℝ → ( 𝐴 + 0 ) = 𝐴 ) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | resubid | ⊢ ( 𝐴 ∈ ℝ → ( 𝐴 −ℝ 𝐴 ) = 0 ) | |
2 | id | ⊢ ( 𝐴 ∈ ℝ → 𝐴 ∈ ℝ ) | |
3 | elre0re | ⊢ ( 𝐴 ∈ ℝ → 0 ∈ ℝ ) | |
4 | 2 2 3 | resubaddd | ⊢ ( 𝐴 ∈ ℝ → ( ( 𝐴 −ℝ 𝐴 ) = 0 ↔ ( 𝐴 + 0 ) = 𝐴 ) ) |
5 | 1 4 | mpbid | ⊢ ( 𝐴 ∈ ℝ → ( 𝐴 + 0 ) = 𝐴 ) |