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Theorem bnj564 29174
Description: First-order logic and set theory. (Contributed by Jonathan Ben-Naim, 3-Jun-2011.) (New usage is discouraged.)
Hypothesis
Ref Expression
bnj564.17  |-  ( ta  <->  ( f  Fn  m  /\  ph' 
/\  ps' ) )
Assertion
Ref Expression
bnj564  |-  ( ta 
->  dom  f  =  m )

Proof of Theorem bnj564
StepHypRef Expression
1 bnj564.17 . . 3  |-  ( ta  <->  ( f  Fn  m  /\  ph' 
/\  ps' ) )
21simp1bi 973 . 2  |-  ( ta 
->  f  Fn  m
)
3 fndm 5546 . 2  |-  ( f  Fn  m  ->  dom  f  =  m )
42, 3syl 16 1  |-  ( ta 
->  dom  f  =  m )
Colors of variables: wff set class
Syntax hints:    -> wi 4    <-> wb 178    /\ w3a 937    = wceq 1653   dom cdm 4880    Fn wfn 5451
This theorem is referenced by:  bnj570  29338  bnj916  29366
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8
This theorem depends on definitions:  df-bi 179  df-an 362  df-3an 939  df-fn 5459
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