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Theorem dffun6f 4858
Description: Definition of function, using bound-variable hypotheses instead of distinct variable conditions. (Contributed by NM, 9-Mar-1995.) (Revised by Mario Carneiro, 15-Oct-2016.)
Hypotheses
Ref Expression
dffun6f.1  F/_
dffun6f.2  F/_
Assertion
Ref Expression
dffun6f  Fun  Rel
Distinct variable group:   ,
Allowed substitution hints:   (,)

Proof of Theorem dffun6f
Dummy variables are mutually distinct and distinct from all other variables.
StepHypRef Expression
1 dffun2 4855 . 2  Fun  Rel
2 nfcv 2175 . . . . . . 7  F/_
3 dffun6f.2 . . . . . . 7  F/_
4 nfcv 2175 . . . . . . 7  F/_
52, 3, 4nfbr 3799 . . . . . 6  F/
6 nfv 1418 . . . . . 6  F/
7 breq2 3759 . . . . . 6
85, 6, 7cbvmo 1937 . . . . 5
98albii 1356 . . . 4
10 breq2 3759 . . . . . 6
1110mo4 1958 . . . . 5
1211albii 1356 . . . 4
13 nfcv 2175 . . . . . . 7  F/_
14 dffun6f.1 . . . . . . 7  F/_
15 nfcv 2175 . . . . . . 7  F/_
1613, 14, 15nfbr 3799 . . . . . 6  F/
1716nfmo 1917 . . . . 5  F/
18 nfv 1418 . . . . 5  F/
19 breq1 3758 . . . . . 6
2019mobidv 1933 . . . . 5
2117, 18, 20cbval 1634 . . . 4
229, 12, 213bitr3ri 200 . . 3
2322anbi2i 430 . 2  Rel  Rel
241, 23bitr4i 176 1  Fun  Rel
Colors of variables: wff set class
Syntax hints:   wi 4   wa 97   wb 98  wal 1240  wmo 1898   F/_wnfc 2162   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:  dffun6  4859  dffun4f  4861  funopab  4878
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