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Theorem ndmaov 28151
Description: The value of an operation outside its domain, analogous to ndmafv 28108. (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
StepHypRef Expression
1 df-aov 28079 . 2  |- (( A F B))  =  ( F''' <. A ,  B >. )
2 ndmafv 28108 . 2  |-  ( -. 
<. A ,  B >.  e. 
dom  F  ->  ( F''' <. A ,  B >. )  =  _V )
31, 2syl5eq 2340 1  |-  ( -. 
<. A ,  B >.  e. 
dom  F  -> (( A F B))  =  _V )
Colors of variables: wff set class
Syntax hints:   -. wn 3    -> wi 4    = wceq 1632    e. wcel 1696   _Vcvv 2801   <.cop 3656   dom cdm 4705  '''cafv 28075   ((caov 28076
This theorem is referenced by:  ndmaovg  28152  ndmaovcl  28171  ndmaovcom  28173  ndmaovass  28174  ndmaovdistr  28175
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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