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Theorem dffun4f 4864
Description: Definition of function like dffun4 4859 but using bound-variable hypotheses instead of distinct variable conditions. (Contributed by Jim Kingdon, 17-Mar-2019.)
Hypotheses
Ref Expression
dffun4f.1  F/_
dffun4f.2  F/_
dffun4f.3  F/_
Assertion
Ref Expression
dffun4f  Fun  Rel  <. ,  >.  <. , 
>.
Distinct variable group:   ,,
Allowed substitution hints:   (,,)

Proof of Theorem dffun4f
Dummy variable is distinct from all other variables.
StepHypRef Expression
1 dffun4f.1 . . 3  F/_
2 dffun4f.2 . . 3  F/_
31, 2dffun6f 4861 . 2  Fun  Rel
4 nfcv 2178 . . . . . . 7  F/_
5 nfcv 2178 . . . . . . 7  F/_
64, 2, 5nfbr 3802 . . . . . 6  F/
7 breq2 3762 . . . . . 6
86, 7mo4f 1960 . . . . 5
9 nfv 1421 . . . . . . 7  F/
10 nfcv 2178 . . . . . . . . . 10  F/_
11 dffun4f.3 . . . . . . . . . 10  F/_
12 nfcv 2178 . . . . . . . . . 10  F/_
1310, 11, 12nfbr 3802 . . . . . . . . 9  F/
14 nfcv 2178 . . . . . . . . . 10  F/_
1510, 11, 14nfbr 3802 . . . . . . . . 9  F/
1613, 15nfan 1457 . . . . . . . 8  F/
17 nfv 1421 . . . . . . . 8  F/
1816, 17nfim 1464 . . . . . . 7  F/
19 breq2 3762 . . . . . . . . 9
2019anbi2d 437 . . . . . . . 8
21 equequ2 1599 . . . . . . . 8
2220, 21imbi12d 223 . . . . . . 7
239, 18, 22cbval 1637 . . . . . 6
2423albii 1359 . . . . 5
258, 24bitr4i 176 . . . 4
2625albii 1359 . . 3
2726anbi2i 430 . 2  Rel  Rel
28 df-br 3759 . . . . . . 7  <. ,  >.
29 df-br 3759 . . . . . . 7  <. ,  >.
3028, 29anbi12i 433 . . . . . 6  <. ,  >.  <. , 
>.
3130imbi1i 227 . . . . 5  <. ,  >.  <. , 
>.
32312albii 1360 . . . 4  <. , 
>.  <. ,  >.
3332albii 1359 . . 3  <. ,  >.  <. , 
>.
3433anbi2i 430 . 2  Rel  Rel  <. ,  >.  <. , 
>.
353, 27, 343bitri 195 1  Fun  Rel  <. ,  >.  <. , 
>.
Colors of variables: wff set class
Syntax hints:   wi 4   wa 97   wb 98  wal 1241   wcel 1393  wmo 1901   F/_wnfc 2165   <.cop 3373   class class class wbr 3758   Rel wrel 4296   Fun wfun 4842
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 3869  ax-pow 3921  ax-pr 3938
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 2308  df-v 2556  df-un 2919  df-in 2921  df-ss 2928  df-pw 3356  df-sn 3376  df-pr 3377  df-op 3379  df-br 3759  df-opab 3813  df-id 4024  df-cnv 4299  df-co 4300  df-fun 4850
This theorem is referenced by: (None)
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