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| Mirrors > Home > MPE Home > Th. List > fexd | Structured version Visualization version GIF version | ||
| Description: If the domain of a mapping is a set, the function is a set. (Contributed by Glauco Siliprandi, 26-Jun-2021.) |
| Ref | Expression |
|---|---|
| fexd.1 | ⊢ (𝜑 → 𝐹:𝐴⟶𝐵) |
| fexd.2 | ⊢ (𝜑 → 𝐴 ∈ 𝐶) |
| Ref | Expression |
|---|---|
| fexd | ⊢ (𝜑 → 𝐹 ∈ V) |
| Step | Hyp | Ref | Expression |
|---|---|---|---|
| 1 | fexd.1 | . 2 ⊢ (𝜑 → 𝐹:𝐴⟶𝐵) | |
| 2 | fexd.2 | . 2 ⊢ (𝜑 → 𝐴 ∈ 𝐶) | |
| 3 | fex 7246 | . 2 ⊢ ((𝐹:𝐴⟶𝐵 ∧ 𝐴 ∈ 𝐶) → 𝐹 ∈ V) | |
| 4 | 1, 2, 3 | syl2anc 584 | 1 ⊢ (𝜑 → 𝐹 ∈ V) |
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