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Mirrors > Home > MPE Home > Th. List > fdm | Structured version Visualization version GIF version |
Description: The domain of a mapping. (Contributed by NM, 2-Aug-1994.) |
Ref | Expression |
---|---|
fdm | ⊢ (𝐹:𝐴⟶𝐵 → dom 𝐹 = 𝐴) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | ffn 6291 | . 2 ⊢ (𝐹:𝐴⟶𝐵 → 𝐹 Fn 𝐴) | |
2 | fndm 6235 | . 2 ⊢ (𝐹 Fn 𝐴 → dom 𝐹 = 𝐴) | |
3 | 1, 2 | syl 17 | 1 ⊢ (𝐹:𝐴⟶𝐵 → dom 𝐹 = 𝐴) |
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