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Theorem funopfv 5461
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 3964 . 2  |-  ( A F B  <->  <. A ,  B >.  e.  F )
2 funbrfv 5460 . 2  |-  ( Fun 
F  ->  ( A F B  ->  ( F `
 A )  =  B ) )
31, 2syl5bir 211 1  |-  ( Fun 
F  ->  ( <. A ,  B >.  e.  F  ->  ( F `  A
)  =  B ) )
Colors of variables: wff set class
Syntax hints:    -> wi 6    = wceq 1619    e. wcel 1621   <.cop 3584   class class class wbr 3963   Fun wfun 4632   ` cfv 4638
This theorem is referenced by:  fvopab3ig  5498  fvsn  5612  fveqf1o  5705  ovidig  5864  ovigg  5867  tfrlem2  6325  fundmen  6867  uzrdg0i  10953  uzrdgsuci  10954  strfvd  13104  strfv2d  13105  imasaddvallem  13358  imasvscafn  13366  adjeq  22440  bnj1379  27875  bnj97  27910  bnj553  27942  bnj966  27988  bnj1442  28091
This theorem was proved from axioms:  ax-1 7  ax-2 8  ax-3 9  ax-mp 10  ax-5 1533  ax-6 1534  ax-7 1535  ax-gen 1536  ax-8 1623  ax-11 1624  ax-14 1626  ax-17 1628  ax-12o 1664  ax-10 1678  ax-9 1684  ax-4 1692  ax-16 1927  ax-ext 2237  ax-sep 4081  ax-nul 4089  ax-pr 4152
This theorem depends on definitions:  df-bi 179  df-or 361  df-an 362  df-3an 941  df-tru 1315  df-ex 1538  df-nf 1540  df-sb 1884  df-eu 2121  df-mo 2122  df-clab 2243  df-cleq 2249  df-clel 2252  df-nfc 2381  df-ne 2421  df-ral 2520  df-rex 2521  df-rab 2523  df-v 2742  df-sbc 2936  df-dif 3097  df-un 3099  df-in 3101  df-ss 3108  df-nul 3398  df-if 3507  df-sn 3587  df-pr 3588  df-op 3590  df-uni 3769  df-br 3964  df-opab 4018  df-id 4246  df-xp 4640  df-rel 4641  df-cnv 4642  df-co 4643  df-dm 4644  df-rn 4645  df-res 4646  df-ima 4647  df-fun 4648  df-fv 4654
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