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Theorem aovfundmoveq 28149
Description: If a class is a function restricted to an ordered pair of its domain, then the value of the operation on this pair is equal for both definitions. (Contributed by Alexander van der Vekens, 26-May-2017.)
Assertion
Ref Expression
aovfundmoveq  |-  ( F defAt  <. A ,  B >.  -> (( A F B))  =  ( A F B ) )

Proof of Theorem aovfundmoveq
StepHypRef Expression
1 afvfundmfveq 28106 . 2  |-  ( F defAt  <. A ,  B >.  -> 
( F''' <. A ,  B >. )  =  ( F `
 <. A ,  B >. ) )
2 df-aov 28079 . 2  |- (( A F B))  =  ( F''' <. A ,  B >. )
3 df-ov 5877 . 2  |-  ( A F B )  =  ( F `  <. A ,  B >. )
41, 2, 33eqtr4g 2353 1  |-  ( F defAt  <. A ,  B >.  -> (( A F B))  =  ( A F B ) )
Colors of variables: wff set class
Syntax hints:    -> wi 4    = wceq 1632   <.cop 3656   ` cfv 5271  (class class class)co 5874   defAt wdfat 28074  '''cafv 28075   ((caov 28076
This theorem is referenced by:  aovmpt4g  28169
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-ov 5877  df-afv 28078  df-aov 28079
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