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| Mirrors > Home > MPE Home > Th. List > fnfvelrn | Structured version Visualization version GIF version | ||
| Description: A function's value belongs to its range. (Contributed by NM, 15-Oct-1996.) |
| Ref | Expression |
|---|---|
| fnfvelrn | ⊢ ((𝐹 Fn 𝐴 ∧ 𝐵 ∈ 𝐴) → (𝐹‘𝐵) ∈ ran 𝐹) |
| Step | Hyp | Ref | Expression |
|---|---|---|---|
| 1 | fvelrn 7096 | . 2 ⊢ ((Fun 𝐹 ∧ 𝐵 ∈ dom 𝐹) → (𝐹‘𝐵) ∈ ran 𝐹) | |
| 2 | 1 | funfni 6674 | 1 ⊢ ((𝐹 Fn 𝐴 ∧ 𝐵 ∈ 𝐴) → (𝐹‘𝐵) ∈ ran 𝐹) |
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