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Theorem aovfundmoveq 27714
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 27671 . 2  |-  ( F defAt  <. A ,  B >.  -> 
( F''' <. A ,  B >. )  =  ( F `
 <. A ,  B >. ) )
2 df-aov 27644 . 2  |- (( A F B))  =  ( F''' <. A ,  B >. )
3 df-ov 6023 . 2  |-  ( A F B )  =  ( F `  <. A ,  B >. )
41, 2, 33eqtr4g 2444 1  |-  ( F defAt  <. A ,  B >.  -> (( A F B))  =  ( A F B ) )
Colors of variables: wff set class
Syntax hints:    -> wi 4    = wceq 1649   <.cop 3760   ` cfv 5394  (class class class)co 6020   defAt wdfat 27639  '''cafv 27640   ((caov 27641
This theorem is referenced by:  aovmpt4g  27734
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1552  ax-5 1563  ax-17 1623  ax-9 1661  ax-8 1682  ax-6 1736  ax-7 1741  ax-11 1753  ax-12 1939  ax-ext 2368
This theorem depends on definitions:  df-bi 178  df-or 360  df-an 361  df-tru 1325  df-ex 1548  df-nf 1551  df-sb 1656  df-clab 2374  df-cleq 2380  df-clel 2383  df-nfc 2512  df-rab 2658  df-v 2901  df-un 3268  df-if 3683  df-fv 5402  df-ov 6023  df-afv 27643  df-aov 27644
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