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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 5173 | . 2 | |
2 | df-id 4254 | . . . . . 6 | |
3 | 2 | sseq2i 3155 | . . . . 5 |
4 | df-co 4596 | . . . . . 6 | |
5 | 4 | sseq1i 3154 | . . . . 5 |
6 | ssopab2b 4237 | . . . . 5 | |
7 | 3, 5, 6 | 3bitri 205 | . . . 4 |
8 | vex 2715 | . . . . . . . . . . . 12 | |
9 | vex 2715 | . . . . . . . . . . . 12 | |
10 | 8, 9 | brcnv 4770 | . . . . . . . . . . 11 |
11 | 10 | anbi1i 454 | . . . . . . . . . 10 |
12 | 11 | exbii 1585 | . . . . . . . . 9 |
13 | 12 | imbi1i 237 | . . . . . . . 8 |
14 | 19.23v 1863 | . . . . . . . 8 | |
15 | 13, 14 | bitr4i 186 | . . . . . . 7 |
16 | 15 | albii 1450 | . . . . . 6 |
17 | alcom 1458 | . . . . . 6 | |
18 | 16, 17 | bitri 183 | . . . . 5 |
19 | 18 | albii 1450 | . . . 4 |
20 | alcom 1458 | . . . 4 | |
21 | 7, 19, 20 | 3bitri 205 | . . 3 |
22 | 21 | anbi2i 453 | . 2 |
23 | 1, 22 | bitri 183 | 1 |
Colors of variables: wff set class |
Syntax hints: wi 4 wa 103 wb 104 wal 1333 wex 1472 wss 3102 class class class wbr 3966 copab 4025 cid 4249 ccnv 4586 ccom 4591 wrel 4592 wfun 5165 |
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 699 ax-5 1427 ax-7 1428 ax-gen 1429 ax-ie1 1473 ax-ie2 1474 ax-8 1484 ax-10 1485 ax-11 1486 ax-i12 1487 ax-bndl 1489 ax-4 1490 ax-17 1506 ax-i9 1510 ax-ial 1514 ax-i5r 1515 ax-14 2131 ax-ext 2139 ax-sep 4083 ax-pow 4136 ax-pr 4170 |
This theorem depends on definitions: df-bi 116 df-3an 965 df-tru 1338 df-nf 1441 df-sb 1743 df-eu 2009 df-mo 2010 df-clab 2144 df-cleq 2150 df-clel 2153 df-nfc 2288 df-ral 2440 df-v 2714 df-un 3106 df-in 3108 df-ss 3115 df-pw 3545 df-sn 3566 df-pr 3567 df-op 3569 df-br 3967 df-opab 4027 df-id 4254 df-cnv 4595 df-co 4596 df-fun 5173 |
This theorem is referenced by: dffun4 5182 dffun6f 5184 sbcfung 5195 funcnveq 5234 fliftfun 5747 fclim 11195 |
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