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Theorem dfimafn2 5169
Description: Alternate definition of the image of a function as an indexed union of singletons of function values. (Contributed by Raph Levien, 20-Nov-2006.)
Assertion
Ref Expression
dfimafn2  Fun  F  C_ 
dom  F  F "  U_  { F `
 }
Distinct variable groups:   ,   , F

Proof of Theorem dfimafn2
Dummy variable is distinct from all other variables.
StepHypRef Expression
1 dfimafn 5168 . . 3  Fun  F  C_ 
dom  F  F "  {  |  F `  }
2 iunab 3697 . . 3  U_  {  |  F `  }  {  |  F `  }
31, 2syl6eqr 2090 . 2  Fun  F  C_ 
dom  F  F "  U_  {  |  F `  }
4 df-sn 3376 . . . . 5  { F `  }  {  |  F `  }
5 eqcom 2042 . . . . . 6  F `  F `
65abbii 2153 . . . . 5  {  |  F `  }  {  |  F `  }
74, 6eqtri 2060 . . . 4  { F `  }  {  |  F `  }
87a1i 9 . . 3  { F `  }  {  |  F `  }
98iuneq2i 3669 . 2  U_  { F `
 }  U_  {  |  F `  }
103, 9syl6eqr 2090 1  Fun  F  C_ 
dom  F  F "  U_  { F `
 }
Colors of variables: wff set class
Syntax hints:   wi 4   wa 97   wceq 1243   wcel 1393   {cab 2026  wrex 2304    C_ wss 2914   {csn 3370   U_ciun 3651   dom cdm 4291   "cima 4294   Fun wfun 4842   ` cfv 4848
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 3869  ax-pow 3921  ax-pr 3938
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 2308  df-rex 2309  df-v 2556  df-sbc 2762  df-un 2919  df-in 2921  df-ss 2928  df-pw 3356  df-sn 3376  df-pr 3377  df-op 3379  df-uni 3575  df-iun 3653  df-br 3759  df-opab 3813  df-id 4024  df-xp 4297  df-rel 4298  df-cnv 4299  df-co 4300  df-dm 4301  df-rn 4302  df-res 4303  df-ima 4304  df-iota 4813  df-fun 4850  df-fn 4851  df-fv 4856
This theorem is referenced by: (None)
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