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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 6655 | . 2 ⊢ (𝐹 Fn 𝐴 → Fun 𝐹) | |
2 | funrel 6571 | . 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 5683 Fun wfun 6543 Fn wfn 6544 |
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 206 df-an 395 df-fun 6551 df-fn 6552 |
This theorem is referenced by: fnbr 6663 fnunres1 6667 fnresdm 6675 fn0 6687 frel 6728 fcoi2 6772 f1rel 6796 f1ocnv 6850 dffn5 6956 feqmptdf 6968 fnsnfvOLD 6977 fconst5 7218 fnex 7229 fnexALT 7955 tz7.48-2 8463 resfnfinfin 9358 zorn2lem4 10524 imasvscafn 17522 2oppchomf 17709 opprabs 33294 bnj66 34622 tfsconcatb0 42915 tfsconcat0i 42916 tfsconcat0b 42917 tfsconcat00 42918 fnresdmss 44680 dfafn5a 46678 |
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