Description: Closure law for the exponential function, deduction version. (Contributed by Thierry Arnoux, 1-Dec-2021)
Ref | Expression | ||
---|---|---|---|
Hypothesis | efcld.1 | ⊢ ( 𝜑 → 𝐴 ∈ ℂ ) | |
Assertion | efcld | ⊢ ( 𝜑 → ( exp ‘ 𝐴 ) ∈ ℂ ) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | efcld.1 | ⊢ ( 𝜑 → 𝐴 ∈ ℂ ) | |
2 | efcl | ⊢ ( 𝐴 ∈ ℂ → ( exp ‘ 𝐴 ) ∈ ℂ ) | |
3 | 1 2 | syl | ⊢ ( 𝜑 → ( exp ‘ 𝐴 ) ∈ ℂ ) |