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Theorem funimass3 6003
 Description: A kind of contraposition law that infers an image subclass from a subclass of a preimage. Raph Levien remarks: "Likely this could be proved directly, and fvimacnv 6002 would be the special case of being a singleton, but it works this way round too." (Contributed by Raph Levien, 20-Nov-2006.)
Assertion
Ref Expression
funimass3

Proof of Theorem funimass3
Dummy variable is distinct from all other variables.
StepHypRef Expression
1 funimass4 5924 . . 3
2 ssel 3497 . . . . . 6
3 fvimacnv 6002 . . . . . . 7
43ex 434 . . . . . 6
52, 4syl9r 72 . . . . 5
65imp31 432 . . . 4
76ralbidva 2893 . . 3
81, 7bitrd 253 . 2
9 dfss3 3493 . 2
108, 9syl6bbr 263 1
 Colors of variables: wff setvar class Syntax hints:  ->wi 4  <->wb 184  /\wa 369  e.wcel 1818  A.wral 2807  C_wss 3475  'ccnv 5003  domcdm 5004  "cima 5007  Funwfun 5587  cfv 5593 This theorem is referenced by:  funimass5  6004  funconstss  6005  fvimacnvALT  6006  fimacnv  6019  r0weon  8411  iscnp3  19745  cnpnei  19765  cnclsi  19773  cncls  19775  cncnp  19781  1stccnp  19963  txcnpi  20109  xkoco2cn  20159  xkococnlem  20160  basqtop  20212  kqnrmlem1  20244  kqnrmlem2  20245  reghmph  20294  nrmhmph  20295  elfm3  20451  rnelfm  20454  symgtgp  20600  tgpconcompeqg  20610  eltsms  20631  ucnprima  20785  plyco0  22589  plyeq0  22608  xrlimcnp  23298  rinvf1o  27472  xppreima  27487  cvmliftmolem1  28726  cvmlift2lem9  28756  cvmlift3lem6  28769  mclsppslem  28943 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1618  ax-4 1631  ax-5 1704  ax-6 1747  ax-7 1790  ax-9 1822  ax-10 1837  ax-11 1842  ax-12 1854  ax-13 1999  ax-ext 2435  ax-sep 4573  ax-nul 4581  ax-pr 4691 This theorem depends on definitions:  df-bi 185  df-or 370  df-an 371  df-3an 975  df-tru 1398  df-ex 1613  df-nf 1617  df-sb 1740  df-eu 2286  df-mo 2287  df-clab 2443  df-cleq 2449  df-clel 2452  df-nfc 2607  df-ne 2654  df-ral 2812  df-rex 2813  df-rab 2816  df-v 3111  df-sbc 3328  df-dif 3478  df-un 3480  df-in 3482  df-ss 3489  df-nul 3785  df-if 3942  df-sn 4030  df-pr 4032  df-op 4036  df-uni 4250  df-br 4453  df-opab 4511  df-id 4800  df-xp 5010  df-rel 5011  df-cnv 5012  df-co 5013  df-dm 5014  df-rn 5015  df-res 5016  df-ima 5017  df-iota 5556  df-fun 5595  df-fn 5596  df-fv 5601
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