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Mirrors > Home > ILE Home > Th. List > dffun4f | Unicode version |
Description: Definition of function like dffun4 5184 but using bound-variable hypotheses instead of distinct variable conditions. (Contributed by Jim Kingdon, 17-Mar-2019.) |
Ref | Expression |
---|---|
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 5186 | . 2 |
4 | nfcv 2299 | . . . . . . 7 | |
5 | nfcv 2299 | . . . . . . 7 | |
6 | 4, 2, 5 | nfbr 4013 | . . . . . 6 |
7 | breq2 3971 | . . . . . 6 | |
8 | 6, 7 | mo4f 2066 | . . . . 5 |
9 | nfv 1508 | . . . . . . 7 | |
10 | nfcv 2299 | . . . . . . . . . 10 | |
11 | dffun4f.3 | . . . . . . . . . 10 | |
12 | nfcv 2299 | . . . . . . . . . 10 | |
13 | 10, 11, 12 | nfbr 4013 | . . . . . . . . 9 |
14 | nfcv 2299 | . . . . . . . . . 10 | |
15 | 10, 11, 14 | nfbr 4013 | . . . . . . . . 9 |
16 | 13, 15 | nfan 1545 | . . . . . . . 8 |
17 | nfv 1508 | . . . . . . . 8 | |
18 | 16, 17 | nfim 1552 | . . . . . . 7 |
19 | breq2 3971 | . . . . . . . . 9 | |
20 | 19 | anbi2d 460 | . . . . . . . 8 |
21 | equequ2 1693 | . . . . . . . 8 | |
22 | 20, 21 | imbi12d 233 | . . . . . . 7 |
23 | 9, 18, 22 | cbval 1734 | . . . . . 6 |
24 | 23 | albii 1450 | . . . . 5 |
25 | 8, 24 | bitr4i 186 | . . . 4 |
26 | 25 | albii 1450 | . . 3 |
27 | 26 | anbi2i 453 | . 2 |
28 | df-br 3968 | . . . . . . 7 | |
29 | df-br 3968 | . . . . . . 7 | |
30 | 28, 29 | anbi12i 456 | . . . . . 6 |
31 | 30 | imbi1i 237 | . . . . 5 |
32 | 31 | 2albii 1451 | . . . 4 |
33 | 32 | albii 1450 | . . 3 |
34 | 33 | anbi2i 453 | . 2 |
35 | 3, 27, 34 | 3bitri 205 | 1 |
Colors of variables: wff set class |
Syntax hints: wi 4 wa 103 wb 104 wal 1333 wmo 2007 wcel 2128 wnfc 2286 cop 3564 class class class wbr 3967 wrel 4594 wfun 5167 |
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 4085 ax-pow 4138 ax-pr 4172 |
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 3546 df-sn 3567 df-pr 3568 df-op 3570 df-br 3968 df-opab 4029 df-id 4256 df-cnv 4597 df-co 4598 df-fun 5175 |
This theorem is referenced by: (None) |
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