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Theorem aovnfundmuv 27921
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 27851 . 2  |- (( A F B))  =  ( F''' <. A ,  B >. )
2 afvnfundmuv 27878 . 2  |-  ( -.  F defAt  <. A ,  B >.  ->  ( F''' <. A ,  B >. )  =  _V )
31, 2syl5eq 2456 1  |-  ( -.  F defAt  <. A ,  B >.  -> (( A F B))  =  _V )
Colors of variables: wff set class
Syntax hints:   -. wn 3    -> wi 4    = wceq 1649   _Vcvv 2924   <.cop 3785   defAt wdfat 27846  '''cafv 27847   ((caov 27848
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1552  ax-5 1563  ax-17 1623  ax-9 1662  ax-8 1683  ax-6 1740  ax-7 1745  ax-11 1757  ax-12 1946  ax-ext 2393
This theorem depends on definitions:  df-bi 178  df-or 360  df-an 361  df-tru 1325  df-ex 1548  df-nf 1551  df-sb 1656  df-clab 2399  df-cleq 2405  df-clel 2408  df-nfc 2537  df-rab 2683  df-v 2926  df-un 3293  df-if 3708  df-fv 5429  df-afv 27850  df-aov 27851
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