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Theorem fssdm 5245
Description: Expressing that a class is a subclass of the domain of a function expressed in maps-to notation, semi-deduction form. (Contributed by AV, 21-Aug-2022.)
Hypotheses
Ref Expression
fssdm.d  |-  D  C_  dom  F
fssdm.f  |-  ( ph  ->  F : A --> B )
Assertion
Ref Expression
fssdm  |-  ( ph  ->  D  C_  A )

Proof of Theorem fssdm
StepHypRef Expression
1 fssdm.d . 2  |-  D  C_  dom  F
2 fssdm.f . . 3  |-  ( ph  ->  F : A --> B )
32fdmd 5237 . 2  |-  ( ph  ->  dom  F  =  A )
41, 3sseqtrid 3113 1  |-  ( ph  ->  D  C_  A )
Colors of variables: wff set class
Syntax hints:    -> wi 4    C_ wss 3037   dom cdm 4499   -->wf 5077
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 105  ax-ia2 106  ax-ia3 107  ax-5 1406  ax-7 1407  ax-gen 1408  ax-ie1 1452  ax-ie2 1453  ax-8 1465  ax-11 1467  ax-4 1470  ax-17 1489  ax-i9 1493  ax-ial 1497  ax-i5r 1498  ax-ext 2097
This theorem depends on definitions:  df-bi 116  df-nf 1420  df-sb 1719  df-clab 2102  df-cleq 2108  df-clel 2111  df-in 3043  df-ss 3050  df-fn 5084  df-f 5085
This theorem is referenced by:  fisumss  11053  cnclima  12234  txcnmpt  12284  xmeter  12425
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