![]() |
Metamath Proof Explorer |
< Previous
Next >
Nearby theorems |
|
Mirrors > Home > MPE Home > Th. List > fdmOLD | Structured version Visualization version GIF version |
Description: Obsolete version of fdm 6499 as of 29-May-2024. (Contributed by NM, 2-Aug-1994.) (Proof modification is discouraged.) (New usage is discouraged.) |
Ref | Expression |
---|---|
fdmOLD | ⊢ (𝐹:𝐴⟶𝐵 → dom 𝐹 = 𝐴) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | ffn 6491 | . 2 ⊢ (𝐹:𝐴⟶𝐵 → 𝐹 Fn 𝐴) | |
2 | fndm 6429 | . 2 ⊢ (𝐹 Fn 𝐴 → dom 𝐹 = 𝐴) | |
3 | 1, 2 | syl 17 | 1 ⊢ (𝐹:𝐴⟶𝐵 → dom 𝐹 = 𝐴) |
Colors of variables: wff setvar class |
Syntax hints: → wi 4 = wceq 1539 dom cdm 5517 Fn wfn 6323 ⟶wf 6324 |
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 210 df-an 401 df-fn 6331 df-f 6332 |
This theorem is referenced by: (None) |
Copyright terms: Public domain | W3C validator |