Theorem aovfundmoveq 41261

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

Step	Hyp	Ref	Expression
1		afvfundmfveq 41218	. 2 |- ( F defAt <. A , B >. -> ( F''' <. A , B >. ) = ( F ` <. A , B >. ) )
2		df-aov 41198	. 2 |- (( A F B)) = ( F''' <. A , B >. )
3		df-ov 6653	. 2 |- ( A F B ) = ( F ` <. A , B >. )
4	1, 2, 3	3eqtr4g 2681	1 |- ( F defAt <. A , B >. -> (( A F B)) = ( A F B ) )

Syntax hints:   -> wi 4   = wceq 1483   <.cop 4183   ` cfv 5888  (class class class)co 6650   defAt wdfat 41193  '''cafv 41194   ((caov 41195

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1722  ax-4 1737  ax-5 1839  ax-6 1888  ax-7 1935  ax-9 1999  ax-10 2019  ax-11 2034  ax-12 2047  ax-13 2246  ax-ext 2602

This theorem depends on definitions:  df-bi 197  df-or 385  df-an 386  df-tru 1486  df-ex 1705  df-nf 1710  df-sb 1881  df-clab 2609  df-cleq 2615  df-clel 2618  df-nfc 2753  df-rab 2921  df-v 3202  df-un 3579  df-if 4087  df-fv 5896  df-ov 6653  df-afv 41197  df-aov 41198

This theorem is referenced by:  aovmpt4g  41281