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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 5125 | . 2 | |
2 | df-id 4215 | . . . . . 6 | |
3 | 2 | sseq2i 3124 | . . . . 5 |
4 | df-co 4548 | . . . . . 6 | |
5 | 4 | sseq1i 3123 | . . . . 5 |
6 | ssopab2b 4198 | . . . . 5 | |
7 | 3, 5, 6 | 3bitri 205 | . . . 4 |
8 | vex 2689 | . . . . . . . . . . . 12 | |
9 | vex 2689 | . . . . . . . . . . . 12 | |
10 | 8, 9 | brcnv 4722 | . . . . . . . . . . 11 |
11 | 10 | anbi1i 453 | . . . . . . . . . 10 |
12 | 11 | exbii 1584 | . . . . . . . . 9 |
13 | 12 | imbi1i 237 | . . . . . . . 8 |
14 | 19.23v 1855 | . . . . . . . 8 | |
15 | 13, 14 | bitr4i 186 | . . . . . . 7 |
16 | 15 | albii 1446 | . . . . . 6 |
17 | alcom 1454 | . . . . . 6 | |
18 | 16, 17 | bitri 183 | . . . . 5 |
19 | 18 | albii 1446 | . . . 4 |
20 | alcom 1454 | . . . 4 | |
21 | 7, 19, 20 | 3bitri 205 | . . 3 |
22 | 21 | anbi2i 452 | . 2 |
23 | 1, 22 | bitri 183 | 1 |
Colors of variables: wff set class |
Syntax hints: wi 4 wa 103 wb 104 wal 1329 wex 1468 wss 3071 class class class wbr 3929 copab 3988 cid 4210 ccnv 4538 ccom 4543 wrel 4544 wfun 5117 |
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 698 ax-5 1423 ax-7 1424 ax-gen 1425 ax-ie1 1469 ax-ie2 1470 ax-8 1482 ax-10 1483 ax-11 1484 ax-i12 1485 ax-bndl 1486 ax-4 1487 ax-14 1492 ax-17 1506 ax-i9 1510 ax-ial 1514 ax-i5r 1515 ax-ext 2121 ax-sep 4046 ax-pow 4098 ax-pr 4131 |
This theorem depends on definitions: df-bi 116 df-3an 964 df-tru 1334 df-nf 1437 df-sb 1736 df-eu 2002 df-mo 2003 df-clab 2126 df-cleq 2132 df-clel 2135 df-nfc 2270 df-ral 2421 df-v 2688 df-un 3075 df-in 3077 df-ss 3084 df-pw 3512 df-sn 3533 df-pr 3534 df-op 3536 df-br 3930 df-opab 3990 df-id 4215 df-cnv 4547 df-co 4548 df-fun 5125 |
This theorem is referenced by: dffun4 5134 dffun6f 5136 sbcfung 5147 funcnveq 5186 fliftfun 5697 fclim 11063 |
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