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Theorem aovfundmoveq 28012
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 27969 . 2  |-  ( F defAt  <. A ,  B >.  -> 
( F''' <. A ,  B >. )  =  ( F `
 <. A ,  B >. ) )
2 df-aov 27943 . 2  |- (( A F B))  =  ( F''' <. A ,  B >. )
3 df-ov 6076 . 2  |-  ( A F B )  =  ( F `  <. A ,  B >. )
41, 2, 33eqtr4g 2492 1  |-  ( F defAt  <. A ,  B >.  -> (( A F B))  =  ( A F B ) )
Colors of variables: wff set class
Syntax hints:    -> wi 4    = wceq 1652   <.cop 3809   ` cfv 5446  (class class class)co 6073   defAt wdfat 27938  '''cafv 27939   ((caov 27940
This theorem is referenced by:  aovmpt4g  28032
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1555  ax-5 1566  ax-17 1626  ax-9 1666  ax-8 1687  ax-6 1744  ax-7 1749  ax-11 1761  ax-12 1950  ax-ext 2416
This theorem depends on definitions:  df-bi 178  df-or 360  df-an 361  df-tru 1328  df-ex 1551  df-nf 1554  df-sb 1659  df-clab 2422  df-cleq 2428  df-clel 2431  df-nfc 2560  df-rab 2706  df-v 2950  df-un 3317  df-if 3732  df-fv 5454  df-ov 6076  df-afv 27942  df-aov 27943
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