Theorem aovfundmoveq

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)

	Ref	Expression
Assertion	aovfundmoveq	⊢ ( 𝐹 defAt ⟨ 𝐴 , 𝐵 ⟩ → (( 𝐴 𝐹 𝐵 )) = ( 𝐴 𝐹 𝐵 ) )

Proof

Step	Hyp	Ref	Expression
1		afvfundmfveq	⊢ ( 𝐹 defAt ⟨ 𝐴 , 𝐵 ⟩ → ( 𝐹 ''' ⟨ 𝐴 , 𝐵 ⟩ ) = ( 𝐹 ‘ ⟨ 𝐴 , 𝐵 ⟩ ) )
2		df-aov	⊢ (( 𝐴 𝐹 𝐵 )) = ( 𝐹 ''' ⟨ 𝐴 , 𝐵 ⟩ )
3		df-ov	⊢ ( 𝐴 𝐹 𝐵 ) = ( 𝐹 ‘ ⟨ 𝐴 , 𝐵 ⟩ )
4	1 2 3	3eqtr4g	⊢ ( 𝐹 defAt ⟨ 𝐴 , 𝐵 ⟩ → (( 𝐴 𝐹 𝐵 )) = ( 𝐴 𝐹 𝐵 ) )