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| Mirrors > Home > MPE Home > Th. List > faccld | Structured version Visualization version GIF version | ||
| Description: Closure of the factorial function, deduction version of faccl 14322. (Contributed by Glauco Siliprandi, 5-Apr-2020.) |
| Ref | Expression |
|---|---|
| faccld.1 | ⊢ (𝜑 → 𝑁 ∈ ℕ0) |
| Ref | Expression |
|---|---|
| faccld | ⊢ (𝜑 → (!‘𝑁) ∈ ℕ) |
| Step | Hyp | Ref | Expression |
|---|---|---|---|
| 1 | faccld.1 | . 2 ⊢ (𝜑 → 𝑁 ∈ ℕ0) | |
| 2 | faccl 14322 | . 2 ⊢ (𝑁 ∈ ℕ0 → (!‘𝑁) ∈ ℕ) | |
| 3 | 1, 2 | syl 17 | 1 ⊢ (𝜑 → (!‘𝑁) ∈ ℕ) |
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