Metamath Proof Explorer
Description: Equality deduction for nested function and operation value.
(Contributed by AV, 23Jul2022)


Ref 
Expression 

Hypothesis 
fvoveq1d.1 
⊢ ( 𝜑 → 𝐴 = 𝐵 ) 

Assertion 
fvoveq1d 
⊢ ( 𝜑 → ( 𝐹 ‘ ( 𝐴 𝑂 𝐶 ) ) = ( 𝐹 ‘ ( 𝐵 𝑂 𝐶 ) ) ) 
Proof
Step 
Hyp 
Ref 
Expression 
1 

fvoveq1d.1 
⊢ ( 𝜑 → 𝐴 = 𝐵 ) 
2 
1

oveq1d 
⊢ ( 𝜑 → ( 𝐴 𝑂 𝐶 ) = ( 𝐵 𝑂 𝐶 ) ) 
3 
2

fveq2d 
⊢ ( 𝜑 → ( 𝐹 ‘ ( 𝐴 𝑂 𝐶 ) ) = ( 𝐹 ‘ ( 𝐵 𝑂 𝐶 ) ) ) 