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Theorem ffnfvf 5579
 Description: A function maps to a class to which all values belong. This version of ffnfv 5578 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 5578 . 2
2 nfcv 2281 . . . 4
3 ffnfvf.1 . . . 4
4 ffnfvf.3 . . . . . 6
5 nfcv 2281 . . . . . 6
64, 5nffv 5431 . . . . 5
7 ffnfvf.2 . . . . 5
86, 7nfel 2290 . . . 4
9 nfv 1508 . . . 4
10 fveq2 5421 . . . . 5
1110eleq1d 2208 . . . 4
122, 3, 8, 9, 11cbvralf 2648 . . 3
1312anbi2i 452 . 2
141, 13bitri 183 1
 Colors of variables: wff set class Syntax hints:   wa 103   wb 104   wcel 1480  wnfc 2268  wral 2416   wfn 5118  wf 5119  cfv 5123 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 105  ax-ia2 106  ax-ia3 107  ax-io 698  ax-5 1423  ax-7 1424  ax-gen 1425  ax-ie1 1469  ax-ie2 1470  ax-8 1482  ax-10 1483  ax-11 1484  ax-i12 1485  ax-bndl 1486  ax-4 1487  ax-14 1492  ax-17 1506  ax-i9 1510  ax-ial 1514  ax-i5r 1515  ax-ext 2121  ax-sep 4046  ax-pow 4098  ax-pr 4131 This theorem depends on definitions:  df-bi 116  df-3an 964  df-tru 1334  df-nf 1437  df-sb 1736  df-eu 2002  df-mo 2003  df-clab 2126  df-cleq 2132  df-clel 2135  df-nfc 2270  df-ral 2421  df-rex 2422  df-v 2688  df-sbc 2910  df-un 3075  df-in 3077  df-ss 3084  df-pw 3512  df-sn 3533  df-pr 3534  df-op 3536  df-uni 3737  df-br 3930  df-opab 3990  df-mpt 3991  df-id 4215  df-xp 4545  df-rel 4546  df-cnv 4547  df-co 4548  df-dm 4549  df-rn 4550  df-iota 5088  df-fun 5125  df-fn 5126  df-f 5127  df-fv 5131 This theorem is referenced by:  ixpf  6614  cc4f  7089
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