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| Mirrors > Home > MPE Home > Th. List > fvresd | Structured version Visualization version GIF version | ||
| Description: The value of a restricted function, deduction version of fvres 6925. (Contributed by Glauco Siliprandi, 8-Apr-2021.) |
| Ref | Expression |
|---|---|
| fvresd.1 | ⊢ (𝜑 → 𝐴 ∈ 𝐵) |
| Ref | Expression |
|---|---|
| fvresd | ⊢ (𝜑 → ((𝐹 ↾ 𝐵)‘𝐴) = (𝐹‘𝐴)) |
| Step | Hyp | Ref | Expression |
|---|---|---|---|
| 1 | fvresd.1 | . 2 ⊢ (𝜑 → 𝐴 ∈ 𝐵) | |
| 2 | fvres 6925 | . 2 ⊢ (𝐴 ∈ 𝐵 → ((𝐹 ↾ 𝐵)‘𝐴) = (𝐹‘𝐴)) | |
| 3 | 1, 2 | syl 17 | 1 ⊢ (𝜑 → ((𝐹 ↾ 𝐵)‘𝐴) = (𝐹‘𝐴)) |
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