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Theorem dffun6f 4915
 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
dffun6f.2
Assertion
Ref Expression
dffun6f
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 4912 . 2
2 nfcv 2178 . . . . . . 7
3 dffun6f.2 . . . . . . 7
4 nfcv 2178 . . . . . . 7
52, 3, 4nfbr 3808 . . . . . 6
6 nfv 1421 . . . . . 6
7 breq2 3768 . . . . . 6
85, 6, 7cbvmo 1940 . . . . 5
98albii 1359 . . . 4
10 breq2 3768 . . . . . 6
1110mo4 1961 . . . . 5
1211albii 1359 . . . 4
13 nfcv 2178 . . . . . . 7
14 dffun6f.1 . . . . . . 7
15 nfcv 2178 . . . . . . 7
1613, 14, 15nfbr 3808 . . . . . 6
1716nfmo 1920 . . . . 5
18 nfv 1421 . . . . 5
19 breq1 3767 . . . . . 6
2019mobidv 1936 . . . . 5
2117, 18, 20cbval 1637 . . . 4
229, 12, 213bitr3ri 200 . . 3
2322anbi2i 430 . 2
241, 23bitr4i 176 1
 Colors of variables: wff set class Syntax hints:   wi 4   wa 97   wb 98  wal 1241  wmo 1901  wnfc 2165   class class class wbr 3764   wrel 4350   wfun 4896 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 3875  ax-pow 3927  ax-pr 3944 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 2311  df-v 2559  df-un 2922  df-in 2924  df-ss 2931  df-pw 3361  df-sn 3381  df-pr 3382  df-op 3384  df-br 3765  df-opab 3819  df-id 4030  df-cnv 4353  df-co 4354  df-fun 4904 This theorem is referenced by:  dffun6  4916  dffun4f  4918  funopab  4935
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