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Theorem ffnfvf 5324
 Description: A function maps to a class to which all values belong. This version of ffnfv 5323 uses bound-variable hypotheses instead of distinct variable conditions. (Contributed by NM, 28-Sep-2006.)
Hypotheses
Ref Expression
ffnfvf.1
ffnfvf.2
ffnfvf.3
Assertion
Ref Expression
ffnfvf

Proof of Theorem ffnfvf
Dummy variable is distinct from all other variables.
StepHypRef Expression
1 ffnfv 5323 . 2
2 nfcv 2178 . . . 4
3 ffnfvf.1 . . . 4
4 ffnfvf.3 . . . . . 6
5 nfcv 2178 . . . . . 6
64, 5nffv 5185 . . . . 5
7 ffnfvf.2 . . . . 5
86, 7nfel 2186 . . . 4
9 nfv 1421 . . . 4
10 fveq2 5178 . . . . 5
1110eleq1d 2106 . . . 4
122, 3, 8, 9, 11cbvralf 2527 . . 3
1312anbi2i 430 . 2
141, 13bitri 173 1
 Colors of variables: wff set class Syntax hints:   wa 97   wb 98   wcel 1393  wnfc 2165  wral 2306   wfn 4897  wf 4898  cfv 4902 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-rex 2312  df-v 2559  df-sbc 2765  df-un 2922  df-in 2924  df-ss 2931  df-pw 3361  df-sn 3381  df-pr 3382  df-op 3384  df-uni 3581  df-br 3765  df-opab 3819  df-mpt 3820  df-id 4030  df-xp 4351  df-rel 4352  df-cnv 4353  df-co 4354  df-dm 4355  df-rn 4356  df-iota 4867  df-fun 4904  df-fn 4905  df-f 4906  df-fv 4910 This theorem is referenced by: (None)
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