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Theorem funopfv 5562
Description: The second element in an ordered pair member of a function is the function's value. (Contributed by NM, 19-Jul-1996.)
Assertion
Ref Expression
funopfv  |-  ( Fun 
F  ->  ( <. A ,  B >.  e.  F  ->  ( F `  A
)  =  B ) )

Proof of Theorem funopfv
StepHypRef Expression
1 df-br 4024 . 2  |-  ( A F B  <->  <. A ,  B >.  e.  F )
2 funbrfv 5561 . 2  |-  ( Fun 
F  ->  ( A F B  ->  ( F `
 A )  =  B ) )
31, 2syl5bir 209 1  |-  ( Fun 
F  ->  ( <. A ,  B >.  e.  F  ->  ( F `  A
)  =  B ) )
Colors of variables: wff set class
Syntax hints:    -> wi 4    = wceq 1623    e. wcel 1684   <.cop 3643   class class class wbr 4023   Fun wfun 5249   ` cfv 5255
This theorem is referenced by:  fvopab3ig  5599  fvsn  5713  fveqf1o  5806  ovidig  5965  ovigg  5968  tfrlem2  6392  fundmen  6934  uzrdg0i  11022  uzrdgsuci  11023  strfvd  13177  strfv2d  13178  imasaddvallem  13431  imasvscafn  13439  adjeq  22515  bnj1379  28863  bnj97  28898  bnj553  28930  bnj966  28976  bnj1442  29079
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1533  ax-5 1544  ax-17 1603  ax-9 1635  ax-8 1643  ax-14 1688  ax-6 1703  ax-7 1708  ax-11 1715  ax-12 1866  ax-ext 2264  ax-sep 4141  ax-nul 4149  ax-pr 4214
This theorem depends on definitions:  df-bi 177  df-or 359  df-an 360  df-3an 936  df-tru 1310  df-ex 1529  df-nf 1532  df-sb 1630  df-eu 2147  df-mo 2148  df-clab 2270  df-cleq 2276  df-clel 2279  df-nfc 2408  df-ne 2448  df-ral 2548  df-rex 2549  df-rab 2552  df-v 2790  df-sbc 2992  df-dif 3155  df-un 3157  df-in 3159  df-ss 3166  df-nul 3456  df-if 3566  df-sn 3646  df-pr 3647  df-op 3649  df-uni 3828  df-br 4024  df-opab 4078  df-id 4309  df-xp 4695  df-rel 4696  df-cnv 4697  df-co 4698  df-dm 4699  df-iota 5219  df-fun 5257  df-fv 5263
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