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Metamath Proof Explorer
Description: Equality deduction for nested function and operation value.
(Contributed by AV, 23-Jul-2022)
|
|
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 ) ) ) |