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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 6916 | . 2 ⊢ ((Fun 𝐹 ∧ 𝐵 ∈ dom 𝐹) → (𝐹‘𝐵) ∈ ran 𝐹) | |
2 | 1 | funfni 6503 | 1 ⊢ ((𝐹 Fn 𝐴 ∧ 𝐵 ∈ 𝐴) → (𝐹‘𝐵) ∈ ran 𝐹) |
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