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| Mirrors > Home > MPE Home > Th. List > fvresi | Structured version Visualization version GIF version | ||
| Description: The value of a restricted identity function. (Contributed by NM, 19-May-2004.) |
| Ref | Expression |
|---|---|
| fvresi | ⊢ (𝐵 ∈ 𝐴 → (( I ↾ 𝐴)‘𝐵) = 𝐵) |
| Step | Hyp | Ref | Expression |
|---|---|---|---|
| 1 | fvres 6925 | . 2 ⊢ (𝐵 ∈ 𝐴 → (( I ↾ 𝐴)‘𝐵) = ( I ‘𝐵)) | |
| 2 | fvi 6985 | . 2 ⊢ (𝐵 ∈ 𝐴 → ( I ‘𝐵) = 𝐵) | |
| 3 | 1, 2 | eqtrd 2777 | 1 ⊢ (𝐵 ∈ 𝐴 → (( I ↾ 𝐴)‘𝐵) = 𝐵) |
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