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Mirrors > Home > ILE Home > Th. List > dffun4f | Unicode version |
Description: Definition of function like dffun4 5239 but using bound-variable hypotheses instead of distinct variable conditions. (Contributed by Jim Kingdon, 17-Mar-2019.) |
Ref | Expression |
---|---|
dffun4f.1 |
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dffun4f.2 |
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dffun4f.3 |
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Ref | Expression |
---|---|
dffun4f |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | dffun4f.1 |
. . 3
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2 | dffun4f.2 |
. . 3
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3 | 1, 2 | dffun6f 5241 |
. 2
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
4 | nfcv 2329 |
. . . . . . 7
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5 | nfcv 2329 |
. . . . . . 7
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6 | 4, 2, 5 | nfbr 4061 |
. . . . . 6
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7 | breq2 4019 |
. . . . . 6
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() | |
8 | 6, 7 | mo4f 2096 |
. . . . 5
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
9 | nfv 1538 |
. . . . . . 7
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() | |
10 | nfcv 2329 |
. . . . . . . . . 10
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11 | dffun4f.3 |
. . . . . . . . . 10
![]() ![]() ![]() ![]() | |
12 | nfcv 2329 |
. . . . . . . . . 10
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13 | 10, 11, 12 | nfbr 4061 |
. . . . . . . . 9
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14 | nfcv 2329 |
. . . . . . . . . 10
![]() ![]() ![]() ![]() | |
15 | 10, 11, 14 | nfbr 4061 |
. . . . . . . . 9
![]() ![]() ![]() ![]() ![]() ![]() |
16 | 13, 15 | nfan 1575 |
. . . . . . . 8
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17 | nfv 1538 |
. . . . . . . 8
![]() ![]() ![]() ![]() ![]() ![]() | |
18 | 16, 17 | nfim 1582 |
. . . . . . 7
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
19 | breq2 4019 |
. . . . . . . . 9
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() | |
20 | 19 | anbi2d 464 |
. . . . . . . 8
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21 | equequ2 1723 |
. . . . . . . 8
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() | |
22 | 20, 21 | imbi12d 234 |
. . . . . . 7
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23 | 9, 18, 22 | cbval 1764 |
. . . . . 6
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24 | 23 | albii 1480 |
. . . . 5
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25 | 8, 24 | bitr4i 187 |
. . . 4
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
26 | 25 | albii 1480 |
. . 3
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27 | 26 | anbi2i 457 |
. 2
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
28 | df-br 4016 |
. . . . . . 7
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() | |
29 | df-br 4016 |
. . . . . . 7
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30 | 28, 29 | anbi12i 460 |
. . . . . 6
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31 | 30 | imbi1i 238 |
. . . . 5
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32 | 31 | 2albii 1481 |
. . . 4
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33 | 32 | albii 1480 |
. . 3
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34 | 33 | anbi2i 457 |
. 2
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35 | 3, 27, 34 | 3bitri 206 |
1
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Colors of variables: wff set class |
Syntax hints: ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-ia1 106 ax-ia2 107 ax-ia3 108 ax-io 710 ax-5 1457 ax-7 1458 ax-gen 1459 ax-ie1 1503 ax-ie2 1504 ax-8 1514 ax-10 1515 ax-11 1516 ax-i12 1517 ax-bndl 1519 ax-4 1520 ax-17 1536 ax-i9 1540 ax-ial 1544 ax-i5r 1545 ax-14 2161 ax-ext 2169 ax-sep 4133 ax-pow 4186 ax-pr 4221 |
This theorem depends on definitions: df-bi 117 df-3an 981 df-tru 1366 df-nf 1471 df-sb 1773 df-eu 2039 df-mo 2040 df-clab 2174 df-cleq 2180 df-clel 2183 df-nfc 2318 df-ral 2470 df-v 2751 df-un 3145 df-in 3147 df-ss 3154 df-pw 3589 df-sn 3610 df-pr 3611 df-op 3613 df-br 4016 df-opab 4077 df-id 4305 df-cnv 4646 df-co 4647 df-fun 5230 |
This theorem is referenced by: (None) |
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