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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 4904 | . 2 | |
2 | df-id 4030 | . . . . . 6 | |
3 | 2 | sseq2i 2970 | . . . . 5 |
4 | df-co 4354 | . . . . . 6 | |
5 | 4 | sseq1i 2969 | . . . . 5 |
6 | ssopab2b 4013 | . . . . 5 | |
7 | 3, 5, 6 | 3bitri 195 | . . . 4 |
8 | vex 2560 | . . . . . . . . . . . 12 | |
9 | vex 2560 | . . . . . . . . . . . 12 | |
10 | 8, 9 | brcnv 4518 | . . . . . . . . . . 11 |
11 | 10 | anbi1i 431 | . . . . . . . . . 10 |
12 | 11 | exbii 1496 | . . . . . . . . 9 |
13 | 12 | imbi1i 227 | . . . . . . . 8 |
14 | 19.23v 1763 | . . . . . . . 8 | |
15 | 13, 14 | bitr4i 176 | . . . . . . 7 |
16 | 15 | albii 1359 | . . . . . 6 |
17 | alcom 1367 | . . . . . 6 | |
18 | 16, 17 | bitri 173 | . . . . 5 |
19 | 18 | albii 1359 | . . . 4 |
20 | alcom 1367 | . . . 4 | |
21 | 7, 19, 20 | 3bitri 195 | . . 3 |
22 | 21 | anbi2i 430 | . 2 |
23 | 1, 22 | bitri 173 | 1 |
Colors of variables: wff set class |
Syntax hints: wi 4 wa 97 wb 98 wal 1241 wex 1381 wss 2917 class class class wbr 3764 copab 3817 cid 4025 ccnv 4344 ccom 4349 wrel 4350 wfun 4896 |
This theorem was proved from axioms: ax-1 5 ax-2 6 ax-mp 7 ax-ia1 99 ax-ia2 100 ax-ia3 101 ax-io 630 ax-5 1336 ax-7 1337 ax-gen 1338 ax-ie1 1382 ax-ie2 1383 ax-8 1395 ax-10 1396 ax-11 1397 ax-i12 1398 ax-bndl 1399 ax-4 1400 ax-14 1405 ax-17 1419 ax-i9 1423 ax-ial 1427 ax-i5r 1428 ax-ext 2022 ax-sep 3875 ax-pow 3927 ax-pr 3944 |
This theorem depends on definitions: df-bi 110 df-3an 887 df-tru 1246 df-nf 1350 df-sb 1646 df-eu 1903 df-mo 1904 df-clab 2027 df-cleq 2033 df-clel 2036 df-nfc 2167 df-ral 2311 df-v 2559 df-un 2922 df-in 2924 df-ss 2931 df-pw 3361 df-sn 3381 df-pr 3382 df-op 3384 df-br 3765 df-opab 3819 df-id 4030 df-cnv 4353 df-co 4354 df-fun 4904 |
This theorem is referenced by: dffun4 4913 dffun6f 4915 sbcfung 4925 funcnveq 4962 fliftfun 5436 fclim 9815 |
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