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Theorem cnvimass 4986
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 4976 . 2  |-  ( `' A " B ) 
C_  ran  `' A
2 dfdm4 4814 . 2  |-  dom  A  =  ran  `' A
31, 2sseqtrri 3190 1  |-  ( `' A " B ) 
C_  dom  A
Colors of variables: wff set class
Syntax hints:    C_ wss 3129   `'ccnv 4621   dom cdm 4622   ran crn 4623   "cima 4625
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 106  ax-ia2 107  ax-ia3 108  ax-io 709  ax-5 1447  ax-7 1448  ax-gen 1449  ax-ie1 1493  ax-ie2 1494  ax-8 1504  ax-10 1505  ax-11 1506  ax-i12 1507  ax-bndl 1509  ax-4 1510  ax-17 1526  ax-i9 1530  ax-ial 1534  ax-i5r 1535  ax-14 2151  ax-ext 2159  ax-sep 4118  ax-pow 4171  ax-pr 4205
This theorem depends on definitions:  df-bi 117  df-3an 980  df-tru 1356  df-nf 1461  df-sb 1763  df-eu 2029  df-mo 2030  df-clab 2164  df-cleq 2170  df-clel 2173  df-nfc 2308  df-ral 2460  df-rex 2461  df-v 2739  df-un 3133  df-in 3135  df-ss 3142  df-pw 3576  df-sn 3597  df-pr 3598  df-op 3600  df-br 4001  df-opab 4062  df-xp 4628  df-cnv 4630  df-dm 4632  df-rn 4633  df-res 4634  df-ima 4635
This theorem is referenced by:  fvimacnvi  5625  elpreima  5630  fconst4m  5731  nn0supp  9204  fisumss  11371  fprodssdc  11569  1arith  12335  cnpnei  13352  cnclima  13356  cnntri  13357  cnntr  13358  cncnp  13363  cnrest2  13369  cndis  13374  txcnmpt  13406  txdis1cn  13411  hmeoimaf1o  13447  xmeter  13569
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