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Theorem funopfv 5414
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 3921 . 2  |-  ( A F B  <->  <. A ,  B >.  e.  F )
2 funbrfv 5413 . 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 3547   class class class wbr 3920   Fun wfun 4586   ` cfv 4592
This theorem is referenced by:  fvopab3ig  5451  fvsn  5565  fveqf1o  5658  ovidig  5817  ovigg  5820  tfrlem2  6278  fundmen  6819  uzrdg0i  10900  uzrdgsuci  10901  strfvd  13051  strfv2d  13052  imasaddvallem  13305  imasvscafn  13313  adjeq  22345  bnj1379  27552  bnj97  27587  bnj553  27619  bnj966  27665  bnj1442  27768
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 1926  ax-ext 2234  ax-sep 4038  ax-nul 4046  ax-pr 4108
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 1883  df-eu 2118  df-mo 2119  df-clab 2240  df-cleq 2246  df-clel 2249  df-nfc 2374  df-ne 2414  df-ral 2513  df-rex 2514  df-rab 2516  df-v 2729  df-sbc 2922  df-dif 3081  df-un 3083  df-in 3085  df-ss 3089  df-nul 3363  df-if 3471  df-sn 3550  df-pr 3551  df-op 3553  df-uni 3728  df-br 3921  df-opab 3975  df-id 4202  df-xp 4594  df-rel 4595  df-cnv 4596  df-co 4597  df-dm 4598  df-rn 4599  df-res 4600  df-ima 4601  df-fun 4602  df-fv 4608
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