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| Mirrors > Home > MPE Home > Th. List > feqmptd | Structured version Visualization version GIF version | ||
| Description: Deduction form of dffn5 6967. (Contributed by Mario Carneiro, 8-Jan-2015.) |
| Ref | Expression |
|---|---|
| feqmptd.1 | ⊢ (𝜑 → 𝐹:𝐴⟶𝐵) |
| Ref | Expression |
|---|---|
| feqmptd | ⊢ (𝜑 → 𝐹 = (𝑥 ∈ 𝐴 ↦ (𝐹‘𝑥))) |
| Step | Hyp | Ref | Expression |
|---|---|---|---|
| 1 | feqmptd.1 | . . 3 ⊢ (𝜑 → 𝐹:𝐴⟶𝐵) | |
| 2 | 1 | ffnd 6737 | . 2 ⊢ (𝜑 → 𝐹 Fn 𝐴) |
| 3 | dffn5 6967 | . 2 ⊢ (𝐹 Fn 𝐴 ↔ 𝐹 = (𝑥 ∈ 𝐴 ↦ (𝐹‘𝑥))) | |
| 4 | 2, 3 | sylib 218 | 1 ⊢ (𝜑 → 𝐹 = (𝑥 ∈ 𝐴 ↦ (𝐹‘𝑥))) |
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