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Theorem aovnfundmuv 28060
Description: If an ordered pair is not in the domain of a class or the class is not a function restricted to the ordered pair, then the operation value for this pair is the universal class. (Contributed by Alexander van der Vekens, 26-May-2017.)
Assertion
Ref Expression
aovnfundmuv  |-  ( -.  F defAt  <. A ,  B >.  -> (( A F B))  =  _V )

Proof of Theorem aovnfundmuv
StepHypRef Expression
1 df-aov 27990 . 2  |- (( A F B))  =  ( F''' <. A ,  B >. )
2 afvnfundmuv 28017 . 2  |-  ( -.  F defAt  <. A ,  B >.  ->  ( F''' <. A ,  B >. )  =  _V )
31, 2syl5eq 2486 1  |-  ( -.  F defAt  <. A ,  B >.  -> (( A F B))  =  _V )
Colors of variables: wff set class
Syntax hints:   -. wn 3    -> wi 4    = wceq 1653   _Vcvv 2962   <.cop 3841   defAt wdfat 27985  '''cafv 27986   ((caov 27987
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1556  ax-5 1567  ax-17 1627  ax-9 1668  ax-8 1689  ax-6 1746  ax-7 1751  ax-11 1763  ax-12 1953  ax-ext 2423
This theorem depends on definitions:  df-bi 179  df-or 361  df-an 362  df-tru 1329  df-ex 1552  df-nf 1555  df-sb 1660  df-clab 2429  df-cleq 2435  df-clel 2438  df-nfc 2567  df-rab 2720  df-v 2964  df-un 3311  df-if 3764  df-fv 5491  df-afv 27989  df-aov 27990
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