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| Mirrors > Home > MPE Home > Th. List > mptex | 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. Inference version of mptexg 7241. (Contributed by NM, 22-Apr-2005.) (Revised by Mario Carneiro, 20-Dec-2013.) |
| Ref | Expression |
|---|---|
| mptex.1 | ⊢ 𝐴 ∈ V |
| Ref | Expression |
|---|---|
| mptex | ⊢ (𝑥 ∈ 𝐴 ↦ 𝐵) ∈ V |
| Step | Hyp | Ref | Expression |
|---|---|---|---|
| 1 | mptex.1 | . 2 ⊢ 𝐴 ∈ V | |
| 2 | mptexg 7241 | . 2 ⊢ (𝐴 ∈ V → (𝑥 ∈ 𝐴 ↦ 𝐵) ∈ V) | |
| 3 | 1, 2 | ax-mp 5 | 1 ⊢ (𝑥 ∈ 𝐴 ↦ 𝐵) ∈ V |
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