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Mirrors > Home > ILE Home > Th. List > dffun4f | Unicode version |
Description: Definition of function like dffun4 4913 but using bound-variable hypotheses instead of distinct variable conditions. (Contributed by Jim Kingdon, 17-Mar-2019.) |
Ref | Expression |
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dffun4f.1 | |
dffun4f.2 | |
dffun4f.3 |
Ref | Expression |
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dffun4f |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | dffun4f.1 | . . 3 | |
2 | dffun4f.2 | . . 3 | |
3 | 1, 2 | dffun6f 4915 | . 2 |
4 | nfcv 2178 | . . . . . . 7 | |
5 | nfcv 2178 | . . . . . . 7 | |
6 | 4, 2, 5 | nfbr 3808 | . . . . . 6 |
7 | breq2 3768 | . . . . . 6 | |
8 | 6, 7 | mo4f 1960 | . . . . 5 |
9 | nfv 1421 | . . . . . . 7 | |
10 | nfcv 2178 | . . . . . . . . . 10 | |
11 | dffun4f.3 | . . . . . . . . . 10 | |
12 | nfcv 2178 | . . . . . . . . . 10 | |
13 | 10, 11, 12 | nfbr 3808 | . . . . . . . . 9 |
14 | nfcv 2178 | . . . . . . . . . 10 | |
15 | 10, 11, 14 | nfbr 3808 | . . . . . . . . 9 |
16 | 13, 15 | nfan 1457 | . . . . . . . 8 |
17 | nfv 1421 | . . . . . . . 8 | |
18 | 16, 17 | nfim 1464 | . . . . . . 7 |
19 | breq2 3768 | . . . . . . . . 9 | |
20 | 19 | anbi2d 437 | . . . . . . . 8 |
21 | equequ2 1599 | . . . . . . . 8 | |
22 | 20, 21 | imbi12d 223 | . . . . . . 7 |
23 | 9, 18, 22 | cbval 1637 | . . . . . 6 |
24 | 23 | albii 1359 | . . . . 5 |
25 | 8, 24 | bitr4i 176 | . . . 4 |
26 | 25 | albii 1359 | . . 3 |
27 | 26 | anbi2i 430 | . 2 |
28 | df-br 3765 | . . . . . . 7 | |
29 | df-br 3765 | . . . . . . 7 | |
30 | 28, 29 | anbi12i 433 | . . . . . 6 |
31 | 30 | imbi1i 227 | . . . . 5 |
32 | 31 | 2albii 1360 | . . . 4 |
33 | 32 | albii 1359 | . . 3 |
34 | 33 | anbi2i 430 | . 2 |
35 | 3, 27, 34 | 3bitri 195 | 1 |
Colors of variables: wff set class |
Syntax hints: wi 4 wa 97 wb 98 wal 1241 wcel 1393 wmo 1901 wnfc 2165 cop 3378 class class class wbr 3764 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: (None) |
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