Theorem nfunsnaov 41266

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

Step	Hyp	Ref	Expression
1		df-aov 41198	. 2 |- (( A F B)) = ( F''' <. A , B >. )
2		nfunsnafv 41222	. 2 |- ( -. Fun ( F |` { <. A , B >. } ) -> ( F''' <. A , B >. ) = _V )
3	1, 2	syl5eq 2668	1 |- ( -. Fun ( F |` { <. A , B >. } ) -> (( A F B)) = _V )

Syntax hints:   -. wn 3   -> wi 4   = wceq 1483   _Vcvv 3200   {csn 4177   <.cop 4183   |` cres 5116   Fun wfun 5882  '''cafv 41194   ((caov 41195

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1722  ax-4 1737  ax-5 1839  ax-6 1888  ax-7 1935  ax-9 1999  ax-10 2019  ax-11 2034  ax-12 2047  ax-13 2246  ax-ext 2602

This theorem depends on definitions:  df-bi 197  df-or 385  df-an 386  df-tru 1486  df-ex 1705  df-nf 1710  df-sb 1881  df-clab 2609  df-cleq 2615  df-clel 2618  df-nfc 2753  df-rab 2921  df-v 3202  df-un 3579  df-if 4087  df-fv 5896  df-dfat 41196  df-afv 41197  df-aov 41198

This theorem is referenced by: (None)