Intuitionistic Logic Explorer |
< Previous
Next >
Nearby theorems |
||
Mirrors > Home > ILE Home > Th. List > dffun4f | Unicode version |
Description: Definition of function like dffun4 5209 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 |
---|---|
dffun4f |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | dffun4f.1 | . . 3 | |
2 | dffun4f.2 | . . 3 | |
3 | 1, 2 | dffun6f 5211 | . 2 |
4 | nfcv 2312 | . . . . . . 7 | |
5 | nfcv 2312 | . . . . . . 7 | |
6 | 4, 2, 5 | nfbr 4035 | . . . . . 6 |
7 | breq2 3993 | . . . . . 6 | |
8 | 6, 7 | mo4f 2079 | . . . . 5 |
9 | nfv 1521 | . . . . . . 7 | |
10 | nfcv 2312 | . . . . . . . . . 10 | |
11 | dffun4f.3 | . . . . . . . . . 10 | |
12 | nfcv 2312 | . . . . . . . . . 10 | |
13 | 10, 11, 12 | nfbr 4035 | . . . . . . . . 9 |
14 | nfcv 2312 | . . . . . . . . . 10 | |
15 | 10, 11, 14 | nfbr 4035 | . . . . . . . . 9 |
16 | 13, 15 | nfan 1558 | . . . . . . . 8 |
17 | nfv 1521 | . . . . . . . 8 | |
18 | 16, 17 | nfim 1565 | . . . . . . 7 |
19 | breq2 3993 | . . . . . . . . 9 | |
20 | 19 | anbi2d 461 | . . . . . . . 8 |
21 | equequ2 1706 | . . . . . . . 8 | |
22 | 20, 21 | imbi12d 233 | . . . . . . 7 |
23 | 9, 18, 22 | cbval 1747 | . . . . . 6 |
24 | 23 | albii 1463 | . . . . 5 |
25 | 8, 24 | bitr4i 186 | . . . 4 |
26 | 25 | albii 1463 | . . 3 |
27 | 26 | anbi2i 454 | . 2 |
28 | df-br 3990 | . . . . . . 7 | |
29 | df-br 3990 | . . . . . . 7 | |
30 | 28, 29 | anbi12i 457 | . . . . . 6 |
31 | 30 | imbi1i 237 | . . . . 5 |
32 | 31 | 2albii 1464 | . . . 4 |
33 | 32 | albii 1463 | . . 3 |
34 | 33 | anbi2i 454 | . 2 |
35 | 3, 27, 34 | 3bitri 205 | 1 |
Colors of variables: wff set class |
Syntax hints: wi 4 wa 103 wb 104 wal 1346 wmo 2020 wcel 2141 wnfc 2299 cop 3586 class class class wbr 3989 wrel 4616 wfun 5192 |
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 704 ax-5 1440 ax-7 1441 ax-gen 1442 ax-ie1 1486 ax-ie2 1487 ax-8 1497 ax-10 1498 ax-11 1499 ax-i12 1500 ax-bndl 1502 ax-4 1503 ax-17 1519 ax-i9 1523 ax-ial 1527 ax-i5r 1528 ax-14 2144 ax-ext 2152 ax-sep 4107 ax-pow 4160 ax-pr 4194 |
This theorem depends on definitions: df-bi 116 df-3an 975 df-tru 1351 df-nf 1454 df-sb 1756 df-eu 2022 df-mo 2023 df-clab 2157 df-cleq 2163 df-clel 2166 df-nfc 2301 df-ral 2453 df-v 2732 df-un 3125 df-in 3127 df-ss 3134 df-pw 3568 df-sn 3589 df-pr 3590 df-op 3592 df-br 3990 df-opab 4051 df-id 4278 df-cnv 4619 df-co 4620 df-fun 5200 |
This theorem is referenced by: (None) |
Copyright terms: Public domain | W3C validator |