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| Mirrors > Home > MPE Home > Th. List > mptexd | Structured version Visualization version GIF version | ||
| Description: If the domain of a function given by maps-to notation is a set, the function is a set. Deduction version of mptexg 7241. (Contributed by Glauco Siliprandi, 24-Dec-2020.) |
| Ref | Expression |
|---|---|
| mptexd.1 | ⊢ (𝜑 → 𝐴 ∈ 𝑉) |
| Ref | Expression |
|---|---|
| mptexd | ⊢ (𝜑 → (𝑥 ∈ 𝐴 ↦ 𝐵) ∈ V) |
| Step | Hyp | Ref | Expression |
|---|---|---|---|
| 1 | mptexd.1 | . 2 ⊢ (𝜑 → 𝐴 ∈ 𝑉) | |
| 2 | mptexg 7241 | . 2 ⊢ (𝐴 ∈ 𝑉 → (𝑥 ∈ 𝐴 ↦ 𝐵) ∈ V) | |
| 3 | 1, 2 | syl 17 | 1 ⊢ (𝜑 → (𝑥 ∈ 𝐴 ↦ 𝐵) ∈ V) |
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