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Theorem dffun4f 4861
Description: Definition of function like dffun4 4856 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 4858 . 2  Fun  Rel
4 nfcv 2175 . . . . . . 7  F/_
5 nfcv 2175 . . . . . . 7  F/_
64, 2, 5nfbr 3799 . . . . . 6  F/
7 breq2 3759 . . . . . 6
86, 7mo4f 1957 . . . . 5
9 nfv 1418 . . . . . . 7  F/
10 nfcv 2175 . . . . . . . . . 10  F/_
11 dffun4f.3 . . . . . . . . . 10  F/_
12 nfcv 2175 . . . . . . . . . 10  F/_
1310, 11, 12nfbr 3799 . . . . . . . . 9  F/
14 nfcv 2175 . . . . . . . . . 10  F/_
1510, 11, 14nfbr 3799 . . . . . . . . 9  F/
1613, 15nfan 1454 . . . . . . . 8  F/
17 nfv 1418 . . . . . . . 8  F/
1816, 17nfim 1461 . . . . . . 7  F/
19 breq2 3759 . . . . . . . . 9
2019anbi2d 437 . . . . . . . 8
21 equequ2 1596 . . . . . . . 8
2220, 21imbi12d 223 . . . . . . 7
239, 18, 22cbval 1634 . . . . . 6
2423albii 1356 . . . . 5
258, 24bitr4i 176 . . . 4
2625albii 1356 . . 3
2726anbi2i 430 . 2  Rel  Rel
28 df-br 3756 . . . . . . 7  <. ,  >.
29 df-br 3756 . . . . . . 7  <. ,  >.
3028, 29anbi12i 433 . . . . . 6  <. ,  >.  <. , 
>.
3130imbi1i 227 . . . . 5  <. ,  >.  <. , 
>.
32312albii 1357 . . . 4  <. , 
>.  <. ,  >.
3332albii 1356 . . 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 1240   wcel 1390  wmo 1898   F/_wnfc 2162   <.cop 3370   class class class wbr 3755   Rel wrel 4293   Fun wfun 4839
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 629  ax-5 1333  ax-7 1334  ax-gen 1335  ax-ie1 1379  ax-ie2 1380  ax-8 1392  ax-10 1393  ax-11 1394  ax-i12 1395  ax-bndl 1396  ax-4 1397  ax-14 1402  ax-17 1416  ax-i9 1420  ax-ial 1424  ax-i5r 1425  ax-ext 2019  ax-sep 3866  ax-pow 3918  ax-pr 3935
This theorem depends on definitions:  df-bi 110  df-3an 886  df-tru 1245  df-nf 1347  df-sb 1643  df-eu 1900  df-mo 1901  df-clab 2024  df-cleq 2030  df-clel 2033  df-nfc 2164  df-ral 2305  df-v 2553  df-un 2916  df-in 2918  df-ss 2925  df-pw 3353  df-sn 3373  df-pr 3374  df-op 3376  df-br 3756  df-opab 3810  df-id 4021  df-cnv 4296  df-co 4297  df-fun 4847
This theorem is referenced by: (None)
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