Theorem ndmaov 41263

Description: The value of an operation outside its domain, analogous to ndmafv 41220. (Contributed by Alexander van der Vekens, 26-May-2017.)

Assertion

Ref	Expression
ndmaov	|- ( -. <. A , B >. e. dom F -> (( A F B)) = _V )

Proof of Theorem ndmaov

Step	Hyp	Ref	Expression
1		df-aov 41198	. 2 |- (( A F B)) = ( F''' <. A , B >. )
2		ndmafv 41220	. 2 |- ( -. <. A , B >. e. dom F -> ( F''' <. A , B >. ) = _V )
3	1, 2	syl5eq 2668	1 |- ( -. <. A , B >. e. dom F -> (( A F B)) = _V )

Syntax hints:   -. wn 3   -> wi 4   = wceq 1483   e. wcel 1990   _Vcvv 3200   <.cop 4183   dom cdm 5114  '''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:  ndmaovg  41264  ndmaovcl  41283  ndmaovcom  41285  ndmaovass  41286  ndmaovdistr  41287