| Metamath Proof Explorer |
< Previous
Next >
Nearby theorems |
||
| Mirrors > Home > MPE Home > Th. List > fmpttd | Structured version Visualization version GIF version | ||
| Description: Version of fmptd 7134 with inlined definition. Domain and codomain of the mapping operation; deduction form. (Contributed by Glauco Siliprandi, 23-Oct-2021.) (Proof shortened by BJ, 16-Aug-2022.) |
| Ref | Expression |
|---|---|
| fmpttd.1 | ⊢ ((𝜑 ∧ 𝑥 ∈ 𝐴) → 𝐵 ∈ 𝐶) |
| Ref | Expression |
|---|---|
| fmpttd | ⊢ (𝜑 → (𝑥 ∈ 𝐴 ↦ 𝐵):𝐴⟶𝐶) |
| Step | Hyp | Ref | Expression |
|---|---|---|---|
| 1 | fmpttd.1 | . 2 ⊢ ((𝜑 ∧ 𝑥 ∈ 𝐴) → 𝐵 ∈ 𝐶) | |
| 2 | eqid 2737 | . 2 ⊢ (𝑥 ∈ 𝐴 ↦ 𝐵) = (𝑥 ∈ 𝐴 ↦ 𝐵) | |
| 3 | 1, 2 | fmptd 7134 | 1 ⊢ (𝜑 → (𝑥 ∈ 𝐴 ↦ 𝐵):𝐴⟶𝐶) |
| Copyright terms: Public domain | W3C validator |