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Mirrors > Home > MPE Home > Th. List > f1dmOLD | Structured version Visualization version GIF version |
Description: Obsolete version of f1dm 6557 as of 29-May-2024. (Contributed by NM, 8-Mar-2014.) (Proof modification is discouraged.) (New usage is discouraged.) |
Ref | Expression |
---|---|
f1dmOLD | ⊢ (𝐹:𝐴–1-1→𝐵 → dom 𝐹 = 𝐴) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | f1fn 6554 | . 2 ⊢ (𝐹:𝐴–1-1→𝐵 → 𝐹 Fn 𝐴) | |
2 | fndm 6429 | . 2 ⊢ (𝐹 Fn 𝐴 → dom 𝐹 = 𝐴) | |
3 | 1, 2 | syl 17 | 1 ⊢ (𝐹:𝐴–1-1→𝐵 → dom 𝐹 = 𝐴) |
Colors of variables: wff setvar class |
Syntax hints: → wi 4 = wceq 1539 dom cdm 5517 Fn wfn 6323 –1-1→wf1 6325 |
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 df-f1 6333 |
This theorem is referenced by: (None) |
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