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| Description: Deduction form of fdm 6745. The domain of a mapping. (Contributed by Glauco Siliprandi, 26-Jun-2021.) | 
| Ref | Expression | 
|---|---|
| fdmd.1 | ⊢ (𝜑 → 𝐹:𝐴⟶𝐵) | 
| Ref | Expression | 
|---|---|
| fdmd | ⊢ (𝜑 → dom 𝐹 = 𝐴) | 
| Step | Hyp | Ref | Expression | 
|---|---|---|---|
| 1 | fdmd.1 | . 2 ⊢ (𝜑 → 𝐹:𝐴⟶𝐵) | |
| 2 | fdm 6745 | . 2 ⊢ (𝐹:𝐴⟶𝐵 → dom 𝐹 = 𝐴) | |
| 3 | 1, 2 | syl 17 | 1 ⊢ (𝜑 → dom 𝐹 = 𝐴) | 
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