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Theorem cnvimass 4906
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 4896 . 2  |-  ( `' A " B ) 
C_  ran  `' A
2 dfdm4 4735 . 2  |-  dom  A  =  ran  `' A
31, 2sseqtrri 3133 1  |-  ( `' A " B ) 
C_  dom  A
Colors of variables: wff set class
Syntax hints:    C_ wss 3072   `'ccnv 4542   dom cdm 4543   ran crn 4544   "cima 4546
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 699  ax-5 1424  ax-7 1425  ax-gen 1426  ax-ie1 1470  ax-ie2 1471  ax-8 1483  ax-10 1484  ax-11 1485  ax-i12 1486  ax-bndl 1487  ax-4 1488  ax-14 1493  ax-17 1507  ax-i9 1511  ax-ial 1515  ax-i5r 1516  ax-ext 2122  ax-sep 4050  ax-pow 4102  ax-pr 4135
This theorem depends on definitions:  df-bi 116  df-3an 965  df-tru 1335  df-nf 1438  df-sb 1737  df-eu 2003  df-mo 2004  df-clab 2127  df-cleq 2133  df-clel 2136  df-nfc 2271  df-ral 2422  df-rex 2423  df-v 2689  df-un 3076  df-in 3078  df-ss 3085  df-pw 3513  df-sn 3534  df-pr 3535  df-op 3537  df-br 3934  df-opab 3994  df-xp 4549  df-cnv 4551  df-dm 4553  df-rn 4554  df-res 4555  df-ima 4556
This theorem is referenced by:  fvimacnvi  5538  elpreima  5543  fconst4m  5644  nn0supp  9049  fisumss  11189  cnpnei  12418  cnclima  12422  cnntri  12423  cnntr  12424  cncnp  12429  cnrest2  12435  cndis  12440  txcnmpt  12472  txdis1cn  12477  hmeoimaf1o  12513  xmeter  12635
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