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Mirrors > Home > MPE Home > Th. List > dffun6 | Structured version Visualization version 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 2979 | . 2 ⊢ Ⅎ𝑥𝐹 | |
2 | nfcv 2979 | . 2 ⊢ Ⅎ𝑦𝐹 | |
3 | 1, 2 | dffun6f 6371 | 1 ⊢ (Fun 𝐹 ↔ (Rel 𝐹 ∧ ∀𝑥∃*𝑦 𝑥𝐹𝑦)) |
Colors of variables: wff setvar class |
Syntax hints: ↔ wb 208 ∧ wa 398 ∀wal 1535 ∃*wmo 2620 class class class wbr 5068 Rel wrel 5562 Fun wfun 6351 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1796 ax-4 1810 ax-5 1911 ax-6 1970 ax-7 2015 ax-8 2116 ax-9 2124 ax-10 2145 ax-11 2161 ax-12 2177 ax-ext 2795 ax-sep 5205 ax-nul 5212 ax-pr 5332 |
This theorem depends on definitions: df-bi 209 df-an 399 df-or 844 df-3an 1085 df-tru 1540 df-ex 1781 df-nf 1785 df-sb 2070 df-mo 2622 df-eu 2654 df-clab 2802 df-cleq 2816 df-clel 2895 df-nfc 2965 df-ral 3145 df-rab 3149 df-v 3498 df-dif 3941 df-un 3943 df-in 3945 df-ss 3954 df-nul 4294 df-if 4470 df-sn 4570 df-pr 4572 df-op 4576 df-br 5069 df-opab 5131 df-id 5462 df-cnv 5565 df-co 5566 df-fun 6359 |
This theorem is referenced by: funmo 6373 dffun7 6384 fununfun 6404 funcnvsn 6406 funcnv2 6424 svrelfun 6428 fnres 6476 nfunsn 6709 dff3 6868 brdom3 9952 nqerf 10354 shftfn 14434 cnextfun 22674 perfdvf 24503 taylf 24951 funressnvmo 43287 |
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