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Theorem cnvimass 4739
Description: A preimage under any class is included in the domain of the class. (Contributed by FL, 29-Jan-2007.)
Assertion
Ref Expression
cnvimass  |-  ( `' A " B ) 
C_  dom  A

Proof of Theorem cnvimass
StepHypRef Expression
1 imassrn 4730 . 2  |-  ( `' A " B ) 
C_  ran  `' A
2 dfdm4 4576 . 2  |-  dom  A  =  ran  `' A
31, 2sseqtr4i 3042 1  |-  ( `' A " B ) 
C_  dom  A
Colors of variables: wff set class
Syntax hints:    C_ wss 2983   `'ccnv 4391   dom cdm 4392   ran crn 4393   "cima 4395
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 104  ax-ia2 105  ax-ia3 106  ax-io 663  ax-5 1377  ax-7 1378  ax-gen 1379  ax-ie1 1423  ax-ie2 1424  ax-8 1436  ax-10 1437  ax-11 1438  ax-i12 1439  ax-bndl 1440  ax-4 1441  ax-14 1446  ax-17 1460  ax-i9 1464  ax-ial 1468  ax-i5r 1469  ax-ext 2065  ax-sep 3917  ax-pow 3969  ax-pr 3993
This theorem depends on definitions:  df-bi 115  df-3an 922  df-tru 1288  df-nf 1391  df-sb 1688  df-eu 1946  df-mo 1947  df-clab 2070  df-cleq 2076  df-clel 2079  df-nfc 2212  df-ral 2358  df-rex 2359  df-v 2612  df-un 2987  df-in 2989  df-ss 2996  df-pw 3403  df-sn 3423  df-pr 3424  df-op 3426  df-br 3807  df-opab 3861  df-xp 4398  df-cnv 4400  df-dm 4402  df-rn 4403  df-res 4404  df-ima 4405
This theorem is referenced by:  fvimacnvi  5334  elpreima  5339  fconst4m  5434  nn0supp  8443
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