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| Mirrors > Home > MPE Home > Th. List > fssdm | Structured version Visualization version GIF version | ||
| Description: Expressing that a class is a subclass of the domain of a function expressed in maps-to notation, semi-deduction form. (Contributed by AV, 21-Aug-2022.) |
| Ref | Expression |
|---|---|
| fssdm.d | ⊢ 𝐷 ⊆ dom 𝐹 |
| fssdm.f | ⊢ (𝜑 → 𝐹:𝐴⟶𝐵) |
| Ref | Expression |
|---|---|
| fssdm | ⊢ (𝜑 → 𝐷 ⊆ 𝐴) |
| Step | Hyp | Ref | Expression |
|---|---|---|---|
| 1 | fssdm.d | . 2 ⊢ 𝐷 ⊆ dom 𝐹 | |
| 2 | fssdm.f | . . 3 ⊢ (𝜑 → 𝐹:𝐴⟶𝐵) | |
| 3 | 2 | fdmd 6746 | . 2 ⊢ (𝜑 → dom 𝐹 = 𝐴) |
| 4 | 1, 3 | sseqtrid 4026 | 1 ⊢ (𝜑 → 𝐷 ⊆ 𝐴) |
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