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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 4924 | . 2 | |
2 | df-id 4048 | . . . . . 6 | |
3 | 2 | sseq2i 3024 | . . . . 5 |
4 | df-co 4372 | . . . . . 6 | |
5 | 4 | sseq1i 3023 | . . . . 5 |
6 | ssopab2b 4031 | . . . . 5 | |
7 | 3, 5, 6 | 3bitri 204 | . . . 4 |
8 | vex 2604 | . . . . . . . . . . . 12 | |
9 | vex 2604 | . . . . . . . . . . . 12 | |
10 | 8, 9 | brcnv 4536 | . . . . . . . . . . 11 |
11 | 10 | anbi1i 445 | . . . . . . . . . 10 |
12 | 11 | exbii 1536 | . . . . . . . . 9 |
13 | 12 | imbi1i 236 | . . . . . . . 8 |
14 | 19.23v 1804 | . . . . . . . 8 | |
15 | 13, 14 | bitr4i 185 | . . . . . . 7 |
16 | 15 | albii 1399 | . . . . . 6 |
17 | alcom 1407 | . . . . . 6 | |
18 | 16, 17 | bitri 182 | . . . . 5 |
19 | 18 | albii 1399 | . . . 4 |
20 | alcom 1407 | . . . 4 | |
21 | 7, 19, 20 | 3bitri 204 | . . 3 |
22 | 21 | anbi2i 444 | . 2 |
23 | 1, 22 | bitri 182 | 1 |
Colors of variables: wff set class |
Syntax hints: wi 4 wa 102 wb 103 wal 1282 wex 1421 wss 2973 class class class wbr 3785 copab 3838 cid 4043 ccnv 4362 ccom 4367 wrel 4368 wfun 4916 |
This theorem was proved from axioms: ax-1 5 ax-2 6 ax-mp 7 ax-ia1 104 ax-ia2 105 ax-ia3 106 ax-io 662 ax-5 1376 ax-7 1377 ax-gen 1378 ax-ie1 1422 ax-ie2 1423 ax-8 1435 ax-10 1436 ax-11 1437 ax-i12 1438 ax-bndl 1439 ax-4 1440 ax-14 1445 ax-17 1459 ax-i9 1463 ax-ial 1467 ax-i5r 1468 ax-ext 2063 ax-sep 3896 ax-pow 3948 ax-pr 3964 |
This theorem depends on definitions: df-bi 115 df-3an 921 df-tru 1287 df-nf 1390 df-sb 1686 df-eu 1944 df-mo 1945 df-clab 2068 df-cleq 2074 df-clel 2077 df-nfc 2208 df-ral 2353 df-v 2603 df-un 2977 df-in 2979 df-ss 2986 df-pw 3384 df-sn 3404 df-pr 3405 df-op 3407 df-br 3786 df-opab 3840 df-id 4048 df-cnv 4371 df-co 4372 df-fun 4924 |
This theorem is referenced by: dffun4 4933 dffun6f 4935 sbcfung 4945 funcnveq 4982 fliftfun 5456 fclim 10133 |
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