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Theorem aovnfundmuv 27553
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 27482 . 2  |- (( A F B))  =  ( F''' <. A ,  B >. )
2 afvnfundmuv 27510 . 2  |-  ( -.  F defAt  <. A ,  B >.  ->  ( F''' <. A ,  B >. )  =  _V )
31, 2syl5eq 2410 1  |-  ( -.  F defAt  <. A ,  B >.  -> (( A F B))  =  _V )
Colors of variables: wff set class
Syntax hints:   -. wn 3    -> wi 4    = wceq 1647   _Vcvv 2873   <.cop 3732   defAt wdfat 27477  '''cafv 27478   ((caov 27479
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1551  ax-5 1562  ax-17 1621  ax-9 1659  ax-8 1680  ax-6 1734  ax-7 1739  ax-11 1751  ax-12 1937  ax-ext 2347
This theorem depends on definitions:  df-bi 177  df-or 359  df-an 360  df-tru 1324  df-ex 1547  df-nf 1550  df-sb 1654  df-clab 2353  df-cleq 2359  df-clel 2362  df-nfc 2491  df-rab 2637  df-v 2875  df-un 3243  df-if 3655  df-fv 5366  df-afv 27481  df-aov 27482
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