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Theorem funimassov 6223
 Description: Membership relation for the values of a function whose image is a subclass. (Contributed by Mario Carneiro, 23-Dec-2013.)
Assertion
Ref Expression
funimassov
Distinct variable groups:   ,,   ,,   ,,   ,,

Proof of Theorem funimassov
Dummy variable is distinct from all other variables.
StepHypRef Expression
1 funimass4 5777 . 2
2 fveq2 5728 . . . . 5
3 df-ov 6084 . . . . 5
42, 3syl6eqr 2486 . . . 4
54eleq1d 2502 . . 3
65ralxp 5016 . 2
71, 6syl6bb 253 1
 Colors of variables: wff set class Syntax hints:   wi 4   wb 177   wa 359   wceq 1652   wcel 1725  wral 2705   wss 3320  cop 3817   cxp 4876   cdm 4878  cima 4881   wfun 5448  cfv 5454  (class class class)co 6081 This theorem is referenced by:  dprd2da  15600  xkococnlem  17691  iscfil2  19219  itg1addlem4  19591  issh2  22711  cvmlift2lem9  24998 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1555  ax-5 1566  ax-17 1626  ax-9 1666  ax-8 1687  ax-14 1729  ax-6 1744  ax-7 1749  ax-11 1761  ax-12 1950  ax-ext 2417  ax-sep 4330  ax-nul 4338  ax-pr 4403 This theorem depends on definitions:  df-bi 178  df-or 360  df-an 361  df-3an 938  df-tru 1328  df-ex 1551  df-nf 1554  df-sb 1659  df-eu 2285  df-mo 2286  df-clab 2423  df-cleq 2429  df-clel 2432  df-nfc 2561  df-ne 2601  df-ral 2710  df-rex 2711  df-rab 2714  df-v 2958  df-sbc 3162  df-csb 3252  df-dif 3323  df-un 3325  df-in 3327  df-ss 3334  df-nul 3629  df-if 3740  df-sn 3820  df-pr 3821  df-op 3823  df-uni 4016  df-iun 4095  df-br 4213  df-opab 4267  df-id 4498  df-xp 4884  df-rel 4885  df-cnv 4886  df-co 4887  df-dm 4888  df-rn 4889  df-res 4890  df-ima 4891  df-iota 5418  df-fun 5456  df-fn 5457  df-fv 5462  df-ov 6084
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