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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 6668 | . 2 ⊢ (𝐹 Fn 𝐴 → Fun 𝐹) | |
| 2 | funrel 6583 | . 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 5690 Fun wfun 6555 Fn wfn 6556 |
| 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 207 df-an 396 df-fun 6563 df-fn 6564 |
| This theorem is referenced by: fnbr 6676 fnunres1 6680 fnresdm 6687 fn0 6699 frel 6741 fcoi2 6783 f1rel 6807 f1ocnv 6860 dffn5 6967 feqmptdf 6979 fconst5 7226 fnex 7237 fnexALT 7975 tz7.48-2 8482 resfnfinfin 9377 zorn2lem4 10539 imasvscafn 17582 2oppchomf 17767 opprabs 33510 bnj66 34874 tfsconcatb0 43357 tfsconcat0i 43358 tfsconcat0b 43359 tfsconcat00 43360 fnresdmss 45173 dfafn5a 47172 |
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