Description: Multiplication by 0. Theorem I.6 of Apostol p. 18. (Contributed by Mario Carneiro, 27-May-2016)
Ref | Expression | ||
---|---|---|---|
Hypothesis | muld.1 | ⊢ ( 𝜑 → 𝐴 ∈ ℂ ) | |
Assertion | mul02d | ⊢ ( 𝜑 → ( 0 · 𝐴 ) = 0 ) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | muld.1 | ⊢ ( 𝜑 → 𝐴 ∈ ℂ ) | |
2 | mul02 | ⊢ ( 𝐴 ∈ ℂ → ( 0 · 𝐴 ) = 0 ) | |
3 | 1 2 | syl | ⊢ ( 𝜑 → ( 0 · 𝐴 ) = 0 ) |