Description: A cancellation law for division. (Contributed by NM, 9-Feb-1995)
Ref | Expression | ||
---|---|---|---|
Hypotheses | divclz.1 | ⊢ 𝐴 ∈ ℂ | |
divclz.2 | ⊢ 𝐵 ∈ ℂ | ||
divcl.3 | ⊢ 𝐵 ≠ 0 | ||
Assertion | divcan2i | ⊢ ( 𝐵 · ( 𝐴 / 𝐵 ) ) = 𝐴 |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | divclz.1 | ⊢ 𝐴 ∈ ℂ | |
2 | divclz.2 | ⊢ 𝐵 ∈ ℂ | |
3 | divcl.3 | ⊢ 𝐵 ≠ 0 | |
4 | 1 2 | divcan2zi | ⊢ ( 𝐵 ≠ 0 → ( 𝐵 · ( 𝐴 / 𝐵 ) ) = 𝐴 ) |
5 | 3 4 | ax-mp | ⊢ ( 𝐵 · ( 𝐴 / 𝐵 ) ) = 𝐴 |