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Theorem nfunsnaov 28154
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 28079 . 2  |- (( A F B))  =  ( F''' <. A ,  B >. )
2 nfunsnafv 28110 . 2  |-  ( -. 
Fun  ( F  |`  { <. A ,  B >. } )  ->  ( F'''
<. A ,  B >. )  =  _V )
31, 2syl5eq 2340 1  |-  ( -. 
Fun  ( F  |`  { <. A ,  B >. } )  -> (( A F B))  =  _V )
Colors of variables: wff set class
Syntax hints:   -. wn 3    -> wi 4    = wceq 1632   _Vcvv 2801   {csn 3653   <.cop 3656    |` cres 4707   Fun wfun 5265  '''cafv 28075   ((caov 28076
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1536  ax-5 1547  ax-17 1606  ax-9 1644  ax-8 1661  ax-6 1715  ax-7 1720  ax-11 1727  ax-12 1878  ax-ext 2277
This theorem depends on definitions:  df-bi 177  df-or 359  df-an 360  df-tru 1310  df-ex 1532  df-nf 1535  df-sb 1639  df-clab 2283  df-cleq 2289  df-clel 2292  df-nfc 2421  df-rab 2565  df-v 2803  df-un 3170  df-if 3579  df-fv 5279  df-dfat 28077  df-afv 28078  df-aov 28079
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