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Mirrors > Home > MPE Home > Th. List > ffvelrni | Structured version Visualization version GIF version |
Description: A function's value belongs to its codomain. (Contributed by NM, 6-Apr-2005.) |
Ref | Expression |
---|---|
ffvrni.1 | ⊢ 𝐹:𝐴⟶𝐵 |
Ref | Expression |
---|---|
ffvelrni | ⊢ (𝐶 ∈ 𝐴 → (𝐹‘𝐶) ∈ 𝐵) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | ffvrni.1 | . 2 ⊢ 𝐹:𝐴⟶𝐵 | |
2 | ffvelrn 6902 | . 2 ⊢ ((𝐹:𝐴⟶𝐵 ∧ 𝐶 ∈ 𝐴) → (𝐹‘𝐶) ∈ 𝐵) | |
3 | 1, 2 | mpan 690 | 1 ⊢ (𝐶 ∈ 𝐴 → (𝐹‘𝐶) ∈ 𝐵) |
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