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Theorem ffnfvf 5898
 Description: A function maps to a class to which all values belong. This version of ffnfv 5897 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 5897 . 2
2 nfcv 2574 . . . 4
3 ffnfvf.1 . . . 4
4 ffnfvf.3 . . . . . 6
5 nfcv 2574 . . . . . 6
64, 5nffv 5738 . . . . 5
7 ffnfvf.2 . . . . 5
86, 7nfel 2582 . . . 4
9 nfv 1630 . . . 4
10 fveq2 5731 . . . . 5
1110eleq1d 2504 . . . 4
122, 3, 8, 9, 11cbvralf 2928 . . 3
1312anbi2i 677 . 2
141, 13bitri 242 1
 Colors of variables: wff set class Syntax hints:   wb 178   wa 360   wcel 1726  wnfc 2561  wral 2707   wfn 5452  wf 5453  cfv 5457 This theorem is referenced by:  ixpf  7087 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1556  ax-5 1567  ax-17 1627  ax-9 1667  ax-8 1688  ax-14 1730  ax-6 1745  ax-7 1750  ax-11 1762  ax-12 1951  ax-ext 2419  ax-sep 4333  ax-nul 4341  ax-pr 4406 This theorem depends on definitions:  df-bi 179  df-or 361  df-an 362  df-3an 939  df-tru 1329  df-ex 1552  df-nf 1555  df-sb 1660  df-eu 2287  df-mo 2288  df-clab 2425  df-cleq 2431  df-clel 2434  df-nfc 2563  df-ne 2603  df-ral 2712  df-rex 2713  df-rab 2716  df-v 2960  df-sbc 3164  df-dif 3325  df-un 3327  df-in 3329  df-ss 3336  df-nul 3631  df-if 3742  df-sn 3822  df-pr 3823  df-op 3825  df-uni 4018  df-br 4216  df-opab 4270  df-mpt 4271  df-id 4501  df-xp 4887  df-rel 4888  df-cnv 4889  df-co 4890  df-dm 4891  df-rn 4892  df-iota 5421  df-fun 5459  df-fn 5460  df-f 5461  df-fv 5465
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