Mathbox for Glauco Siliprandi |
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Mirrors > Home > MPE Home > Th. List > Mathboxes > fdmd | Structured version Visualization version GIF version |
Description: 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 6051 | . 2 ⊢ (𝐹:𝐴⟶𝐵 → dom 𝐹 = 𝐴) | |
3 | 1, 2 | syl 17 | 1 ⊢ (𝜑 → dom 𝐹 = 𝐴) |
Colors of variables: wff setvar class |
Syntax hints: → wi 4 = wceq 1483 dom cdm 5114 ⟶wf 5884 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 |
This theorem depends on definitions: df-bi 197 df-an 386 df-fn 5891 df-f 5892 |
This theorem is referenced by: limsuppnfdlem 39933 limsupvaluz 39940 climxrrelem 39981 climxrre 39982 liminfvalxr 40015 xlimmnfvlem2 40059 xlimpnfvlem2 40063 issmfd 40944 issmfdf 40946 cnfsmf 40949 issmfled 40966 smfmbfcex 40968 issmfgtd 40969 smfsuplem1 41017 |
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