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Mirrors > Home > ILE Home > Th. List > dffun6 | GIF version |
Description: Alternate definition of a function using "at most one" notation. (Contributed by NM, 9-Mar-1995.) |
Ref | Expression |
---|---|
dffun6 | ⊢ (Fun 𝐹 ↔ (Rel 𝐹 ∧ ∀𝑥∃*𝑦 𝑥𝐹𝑦)) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | nfcv 2312 | . 2 ⊢ Ⅎ𝑥𝐹 | |
2 | nfcv 2312 | . 2 ⊢ Ⅎ𝑦𝐹 | |
3 | 1, 2 | dffun6f 5211 | 1 ⊢ (Fun 𝐹 ↔ (Rel 𝐹 ∧ ∀𝑥∃*𝑦 𝑥𝐹𝑦)) |
Colors of variables: wff set class |
Syntax hints: ∧ wa 103 ↔ wb 104 ∀wal 1346 ∃*wmo 2020 class class class wbr 3989 Rel wrel 4616 Fun wfun 5192 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-ia1 105 ax-ia2 106 ax-ia3 107 ax-io 704 ax-5 1440 ax-7 1441 ax-gen 1442 ax-ie1 1486 ax-ie2 1487 ax-8 1497 ax-10 1498 ax-11 1499 ax-i12 1500 ax-bndl 1502 ax-4 1503 ax-17 1519 ax-i9 1523 ax-ial 1527 ax-i5r 1528 ax-14 2144 ax-ext 2152 ax-sep 4107 ax-pow 4160 ax-pr 4194 |
This theorem depends on definitions: df-bi 116 df-3an 975 df-tru 1351 df-nf 1454 df-sb 1756 df-eu 2022 df-mo 2023 df-clab 2157 df-cleq 2163 df-clel 2166 df-nfc 2301 df-ral 2453 df-v 2732 df-un 3125 df-in 3127 df-ss 3134 df-pw 3568 df-sn 3589 df-pr 3590 df-op 3592 df-br 3990 df-opab 4051 df-id 4278 df-cnv 4619 df-co 4620 df-fun 5200 |
This theorem is referenced by: funmo 5213 dffun7 5225 funcnvsn 5243 funcnv2 5258 svrelfun 5263 fnres 5314 nfunsn 5530 shftfn 10788 dvfgg 13451 |
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