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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 5902 | . 2 ⊢ (𝐹 Fn 𝐴 → Fun 𝐹) | |
2 | funrel 5821 | . 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 5043 Fun wfun 5798 Fn wfn 5799 |
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 196 df-an 385 df-fun 5806 df-fn 5807 |
This theorem is referenced by: fnbr 5907 fnresdm 5914 fn0 5924 frel 5963 fcoi2 5992 f1rel 6017 f1ocnv 6062 dffn5 6151 feqmptdf 6161 fnsnfv 6168 fconst5 6376 fnex 6386 fnexALT 7025 tz7.48-2 7424 zorn2lem4 9204 imasvscafn 16020 2oppchomf 16207 idssxp 28811 bnj66 30184 rtrclex 36943 fnresdmss 38342 dfafn5a 39889 resfnfinfin 40339 |
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