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Mirrors > Home > MPE Home > Th. List > funfnd | Structured version Visualization version GIF version |
Description: A function is a function over its domain. (Contributed by Glauco Siliprandi, 23-Oct-2021.) |
Ref | Expression |
---|---|
funfnd.1 | ⊢ (𝜑 → Fun 𝐴) |
Ref | Expression |
---|---|
funfnd | ⊢ (𝜑 → 𝐴 Fn dom 𝐴) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | funfnd.1 | . 2 ⊢ (𝜑 → Fun 𝐴) | |
2 | funfn 6061 | . 2 ⊢ (Fun 𝐴 ↔ 𝐴 Fn dom 𝐴) | |
3 | 1, 2 | sylib 208 | 1 ⊢ (𝜑 → 𝐴 Fn dom 𝐴) |
Colors of variables: wff setvar class |
Syntax hints: → wi 4 dom cdm 5249 Fun wfun 6025 Fn wfn 6026 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1870 ax-4 1885 ax-5 1991 ax-6 2057 ax-7 2093 ax-9 2154 ax-ext 2751 |
This theorem depends on definitions: df-bi 197 df-an 383 df-ex 1853 df-cleq 2764 df-fn 6034 |
This theorem is referenced by: wfrlem4 7570 uhgrvtxedgiedgb 26252 ushgredgedgloop 26345 upgrres 26421 umgrres 26422 funimaeq 39979 limsupresxr 40516 liminfresxr 40517 |
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