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Theorem ndmaov 28037
Description: The value of an operation outside its domain, analogous to ndmafv 27994. (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 27966 . 2  |- (( A F B))  =  ( F''' <. A ,  B >. )
2 ndmafv 27994 . 2  |-  ( -. 
<. A ,  B >.  e. 
dom  F  ->  ( F''' <. A ,  B >. )  =  _V )
31, 2syl5eq 2482 1  |-  ( -. 
<. A ,  B >.  e. 
dom  F  -> (( A F B))  =  _V )
Colors of variables: wff set class
Syntax hints:   -. wn 3    -> wi 4    = wceq 1653    e. wcel 1726   _Vcvv 2958   <.cop 3819   dom cdm 4881  '''cafv 27962   ((caov 27963
This theorem is referenced by:  ndmaovg  28038  ndmaovcl  28057  ndmaovcom  28059  ndmaovass  28060  ndmaovdistr  28061
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 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 2419
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 2425  df-cleq 2431  df-clel 2434  df-nfc 2563  df-rab 2716  df-v 2960  df-un 3327  df-if 3742  df-fv 5465  df-dfat 27964  df-afv 27965  df-aov 27966
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