Mathbox for Glauco Siliprandi |
< Previous
Next >
Nearby theorems |
||
Mirrors > Home > MPE Home > Th. List > Mathboxes > fndmd | Structured version Visualization version GIF version |
Description: The domain of a function. (Contributed by Glauco Siliprandi, 23-Oct-2021.) |
Ref | Expression |
---|---|
fndmd.1 | ⊢ (𝜑 → 𝐹 Fn 𝐴) |
Ref | Expression |
---|---|
fndmd | ⊢ (𝜑 → dom 𝐹 = 𝐴) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | fndmd.1 | . 2 ⊢ (𝜑 → 𝐹 Fn 𝐴) | |
2 | fndm 5990 | . 2 ⊢ (𝐹 Fn 𝐴 → 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 Fn wfn 5883 |
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 |
This theorem is referenced by: fvelimad 39458 fnfvimad 39459 limsupequzlem 39954 climrescn 39980 smflimmpt 41016 smflimsuplem7 41032 |
Copyright terms: Public domain | W3C validator |