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Mirrors > Home > MPE Home > Th. List > fnrel | Structured version Visualization version GIF version |
Description: A function with domain is a relation. (Contributed by NM, 1-Aug-1994.) |
Ref | Expression |
---|---|
fnrel | ⊢ (𝐹 Fn 𝐴 → Rel 𝐹) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | fnfun 6447 | . 2 ⊢ (𝐹 Fn 𝐴 → Fun 𝐹) | |
2 | funrel 6366 | . 2 ⊢ (Fun 𝐹 → Rel 𝐹) | |
3 | 1, 2 | syl 17 | 1 ⊢ (𝐹 Fn 𝐴 → Rel 𝐹) |
Colors of variables: wff setvar class |
Syntax hints: → wi 4 Rel wrel 5554 Fun wfun 6343 Fn wfn 6344 |
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 208 df-an 397 df-fun 6351 df-fn 6352 |
This theorem is referenced by: fnbr 6453 fnresdm 6460 fn0 6473 frel 6513 fcoi2 6547 f1rel 6572 f1ocnv 6621 dffn5 6718 feqmptdf 6729 fnsnfv 6737 fconst5 6961 fnex 6972 fnexALT 7643 tz7.48-2 8069 resfnfinfin 8793 zorn2lem4 9910 imasvscafn 16800 2oppchomf 16984 fnunres1 30285 bnj66 32032 fnimasnd 39001 fnresdmss 41304 dfafn5a 43240 |
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