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Theorem nfunsnaov 28027
Description: If the restriction of a class to a singleton is not a function, its operation value is the universal class. (Contributed by Alexander van der Vekens, 26-May-2017.)
Assertion
Ref Expression
nfunsnaov  |-  ( -. 
Fun  ( F  |`  { <. A ,  B >. } )  -> (( A F B))  =  _V )

Proof of Theorem nfunsnaov
StepHypRef Expression
1 df-aov 27953 . 2  |- (( A F B))  =  ( F''' <. A ,  B >. )
2 nfunsnafv 27983 . 2  |-  ( -. 
Fun  ( F  |`  { <. A ,  B >. } )  ->  ( F'''
<. A ,  B >. )  =  _V )
31, 2syl5eq 2481 1  |-  ( -. 
Fun  ( F  |`  { <. A ,  B >. } )  -> (( A F B))  =  _V )
Colors of variables: wff set class
Syntax hints:   -. wn 3    -> wi 4    = wceq 1653   _Vcvv 2957   {csn 3815   <.cop 3818    |` cres 4881   Fun wfun 5449  '''cafv 27949   ((caov 27950
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1556  ax-5 1567  ax-17 1627  ax-9 1667  ax-8 1688  ax-6 1745  ax-7 1750  ax-11 1762  ax-12 1951  ax-ext 2418
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 2424  df-cleq 2430  df-clel 2433  df-nfc 2562  df-rab 2715  df-v 2959  df-un 3326  df-if 3741  df-fv 5463  df-dfat 27951  df-afv 27952  df-aov 27953
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