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| Mirrors > Home > MPE Home > Th. List > fssresd | Structured version Visualization version GIF version | ||
| Description: Restriction of a function with a subclass of its domain, deduction form. (Contributed by Glauco Siliprandi, 11-Dec-2019.) |
| Ref | Expression |
|---|---|
| fssresd.1 | ⊢ (𝜑 → 𝐹:𝐴⟶𝐵) |
| fssresd.2 | ⊢ (𝜑 → 𝐶 ⊆ 𝐴) |
| Ref | Expression |
|---|---|
| fssresd | ⊢ (𝜑 → (𝐹 ↾ 𝐶):𝐶⟶𝐵) |
| Step | Hyp | Ref | Expression |
|---|---|---|---|
| 1 | fssresd.1 | . 2 ⊢ (𝜑 → 𝐹:𝐴⟶𝐵) | |
| 2 | fssresd.2 | . 2 ⊢ (𝜑 → 𝐶 ⊆ 𝐴) | |
| 3 | fssres 6774 | . 2 ⊢ ((𝐹:𝐴⟶𝐵 ∧ 𝐶 ⊆ 𝐴) → (𝐹 ↾ 𝐶):𝐶⟶𝐵) | |
| 4 | 1, 2, 3 | syl2anc 584 | 1 ⊢ (𝜑 → (𝐹 ↾ 𝐶):𝐶⟶𝐵) |
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