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Theorem cnvimass 4872
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 4862 . 2  |-  ( `' A " B ) 
C_  ran  `' A
2 dfdm4 4701 . 2  |-  dom  A  =  ran  `' A
31, 2sseqtrri 3102 1  |-  ( `' A " B ) 
C_  dom  A
Colors of variables: wff set class
Syntax hints:    C_ wss 3041   `'ccnv 4508   dom cdm 4509   ran crn 4510   "cima 4512
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 105  ax-ia2 106  ax-ia3 107  ax-io 683  ax-5 1408  ax-7 1409  ax-gen 1410  ax-ie1 1454  ax-ie2 1455  ax-8 1467  ax-10 1468  ax-11 1469  ax-i12 1470  ax-bndl 1471  ax-4 1472  ax-14 1477  ax-17 1491  ax-i9 1495  ax-ial 1499  ax-i5r 1500  ax-ext 2099  ax-sep 4016  ax-pow 4068  ax-pr 4101
This theorem depends on definitions:  df-bi 116  df-3an 949  df-tru 1319  df-nf 1422  df-sb 1721  df-eu 1980  df-mo 1981  df-clab 2104  df-cleq 2110  df-clel 2113  df-nfc 2247  df-ral 2398  df-rex 2399  df-v 2662  df-un 3045  df-in 3047  df-ss 3054  df-pw 3482  df-sn 3503  df-pr 3504  df-op 3506  df-br 3900  df-opab 3960  df-xp 4515  df-cnv 4517  df-dm 4519  df-rn 4520  df-res 4521  df-ima 4522
This theorem is referenced by:  fvimacnvi  5502  elpreima  5507  fconst4m  5608  nn0supp  8997  fisumss  11129  cnpnei  12315  cnclima  12319  cnntri  12320  cnntr  12321  cncnp  12326  cnrest2  12332  cndis  12337  txcnmpt  12369  txdis1cn  12374  hmeoimaf1o  12410  xmeter  12532
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