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| Mirrors > Home > MPE Home > Th. List > fssd | Structured version Visualization version GIF version | ||
| Description: Expanding the codomain of a mapping, deduction form. (Contributed by Glauco Siliprandi, 11-Dec-2019.) |
| Ref | Expression |
|---|---|
| fssd.f | ⊢ (𝜑 → 𝐹:𝐴⟶𝐵) |
| fssd.b | ⊢ (𝜑 → 𝐵 ⊆ 𝐶) |
| Ref | Expression |
|---|---|
| fssd | ⊢ (𝜑 → 𝐹:𝐴⟶𝐶) |
| Step | Hyp | Ref | Expression |
|---|---|---|---|
| 1 | fssd.f | . 2 ⊢ (𝜑 → 𝐹:𝐴⟶𝐵) | |
| 2 | fssd.b | . 2 ⊢ (𝜑 → 𝐵 ⊆ 𝐶) | |
| 3 | fss 6752 | . 2 ⊢ ((𝐹:𝐴⟶𝐵 ∧ 𝐵 ⊆ 𝐶) → 𝐹:𝐴⟶𝐶) | |
| 4 | 1, 2, 3 | syl2anc 584 | 1 ⊢ (𝜑 → 𝐹:𝐴⟶𝐶) |
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