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Mirrors > Home > ILE Home > Th. List > dffun2 | Unicode version |
Description: Alternate definition of a function. (Contributed by NM, 29-Dec-1996.) |
Ref | Expression |
---|---|
dffun2 |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | df-fun 5200 | . 2 | |
2 | df-id 4278 | . . . . . 6 | |
3 | 2 | sseq2i 3174 | . . . . 5 |
4 | df-co 4620 | . . . . . 6 | |
5 | 4 | sseq1i 3173 | . . . . 5 |
6 | ssopab2b 4261 | . . . . 5 | |
7 | 3, 5, 6 | 3bitri 205 | . . . 4 |
8 | vex 2733 | . . . . . . . . . . . 12 | |
9 | vex 2733 | . . . . . . . . . . . 12 | |
10 | 8, 9 | brcnv 4794 | . . . . . . . . . . 11 |
11 | 10 | anbi1i 455 | . . . . . . . . . 10 |
12 | 11 | exbii 1598 | . . . . . . . . 9 |
13 | 12 | imbi1i 237 | . . . . . . . 8 |
14 | 19.23v 1876 | . . . . . . . 8 | |
15 | 13, 14 | bitr4i 186 | . . . . . . 7 |
16 | 15 | albii 1463 | . . . . . 6 |
17 | alcom 1471 | . . . . . 6 | |
18 | 16, 17 | bitri 183 | . . . . 5 |
19 | 18 | albii 1463 | . . . 4 |
20 | alcom 1471 | . . . 4 | |
21 | 7, 19, 20 | 3bitri 205 | . . 3 |
22 | 21 | anbi2i 454 | . 2 |
23 | 1, 22 | bitri 183 | 1 |
Colors of variables: wff set class |
Syntax hints: wi 4 wa 103 wb 104 wal 1346 wex 1485 wss 3121 class class class wbr 3989 copab 4049 cid 4273 ccnv 4610 ccom 4615 wrel 4616 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: dffun4 5209 dffun6f 5211 sbcfung 5222 funcnveq 5261 fliftfun 5775 fclim 11257 |
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