Description: Subtraction of a real number from itself (compare subid ). (Contributed by SN, 23-Jan-2024)
Ref | Expression | ||
---|---|---|---|
Assertion | resubid | ⊢ ( 𝐴 ∈ ℝ → ( 𝐴 −ℝ 𝐴 ) = 0 ) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | re0m0e0 | ⊢ ( 0 −ℝ 0 ) = 0 | |
2 | 1 | oveq2i | ⊢ ( 𝐴 · ( 0 −ℝ 0 ) ) = ( 𝐴 · 0 ) |
3 | sn-00idlem1 | ⊢ ( 𝐴 ∈ ℝ → ( 𝐴 · ( 0 −ℝ 0 ) ) = ( 𝐴 −ℝ 𝐴 ) ) | |
4 | remul01 | ⊢ ( 𝐴 ∈ ℝ → ( 𝐴 · 0 ) = 0 ) | |
5 | 2 3 4 | 3eqtr3a | ⊢ ( 𝐴 ∈ ℝ → ( 𝐴 −ℝ 𝐴 ) = 0 ) |