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Theorem funopfv 5578
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 4040 . 2  |-  ( A F B  <->  <. A ,  B >.  e.  F )
2 funbrfv 5577 . 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 1632    e. wcel 1696   <.cop 3656   class class class wbr 4039   Fun wfun 5265   ` cfv 5271
This theorem is referenced by:  fvopab3ig  5615  fvsn  5729  fveqf1o  5822  ovidig  5981  ovigg  5984  tfrlem2  6408  fundmen  6950  uzrdg0i  11038  uzrdgsuci  11039  strfvd  13193  strfv2d  13194  imasaddvallem  13447  imasvscafn  13455  adjeq  22531  bnj1379  29179  bnj97  29214  bnj553  29246  bnj966  29292  bnj1442  29395
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1536  ax-5 1547  ax-17 1606  ax-9 1644  ax-8 1661  ax-14 1700  ax-6 1715  ax-7 1720  ax-11 1727  ax-12 1878  ax-ext 2277  ax-sep 4157  ax-nul 4165  ax-pr 4230
This theorem depends on definitions:  df-bi 177  df-or 359  df-an 360  df-3an 936  df-tru 1310  df-ex 1532  df-nf 1535  df-sb 1639  df-eu 2160  df-mo 2161  df-clab 2283  df-cleq 2289  df-clel 2292  df-nfc 2421  df-ne 2461  df-ral 2561  df-rex 2562  df-rab 2565  df-v 2803  df-sbc 3005  df-dif 3168  df-un 3170  df-in 3172  df-ss 3179  df-nul 3469  df-if 3579  df-sn 3659  df-pr 3660  df-op 3662  df-uni 3844  df-br 4040  df-opab 4094  df-id 4325  df-xp 4711  df-rel 4712  df-cnv 4713  df-co 4714  df-dm 4715  df-iota 5235  df-fun 5273  df-fv 5279
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