Description: Multiplication of a number and its reciprocal. (Contributed by NM, 14-May-1999)
Ref | Expression | ||
---|---|---|---|
Hypothesis | divclz.1 | ⊢ 𝐴 ∈ ℂ | |
Assertion | recidzi | ⊢ ( 𝐴 ≠ 0 → ( 𝐴 · ( 1 / 𝐴 ) ) = 1 ) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | divclz.1 | ⊢ 𝐴 ∈ ℂ | |
2 | recid | ⊢ ( ( 𝐴 ∈ ℂ ∧ 𝐴 ≠ 0 ) → ( 𝐴 · ( 1 / 𝐴 ) ) = 1 ) | |
3 | 1 2 | mpan | ⊢ ( 𝐴 ≠ 0 → ( 𝐴 · ( 1 / 𝐴 ) ) = 1 ) |