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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 6283 | . 2 ⊢ (𝐹 Fn 𝐴 → Fun 𝐹) | |
2 | funrel 6202 | . 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 5408 Fun wfun 6179 Fn wfn 6180 |
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 199 df-an 388 df-fun 6187 df-fn 6188 |
This theorem is referenced by: fnbr 6289 fnresdm 6296 fn0 6306 frel 6346 fcoi2 6379 f1rel 6404 f1ocnv 6453 dffn5 6551 feqmptdf 6562 fnsnfv 6569 fconst5 6793 fnex 6804 fnexALT 7462 tz7.48-2 7879 resfnfinfin 8597 zorn2lem4 9717 imasvscafn 16664 2oppchomf 16864 fnunres1 30137 bnj66 31811 fnimasnd 38604 rtrclex 39378 fnresdmss 40883 dfafn5a 42799 |
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