| Metamath Proof Explorer |
< Previous
Next >
Nearby theorems |
||
| Mirrors > Home > MPE Home > Th. List > fvoveq1d | Structured version Visualization version GIF version | ||
| Description: Equality deduction for nested function and operation value. (Contributed by AV, 23-Jul-2022.) |
| Ref | Expression |
|---|---|
| fvoveq1d.1 | ⊢ (𝜑 → 𝐴 = 𝐵) |
| Ref | Expression |
|---|---|
| fvoveq1d | ⊢ (𝜑 → (𝐹‘(𝐴𝑂𝐶)) = (𝐹‘(𝐵𝑂𝐶))) |
| Step | Hyp | Ref | Expression |
|---|---|---|---|
| 1 | fvoveq1d.1 | . . 3 ⊢ (𝜑 → 𝐴 = 𝐵) | |
| 2 | 1 | oveq1d 7446 | . 2 ⊢ (𝜑 → (𝐴𝑂𝐶) = (𝐵𝑂𝐶)) |
| 3 | 2 | fveq2d 6910 | 1 ⊢ (𝜑 → (𝐹‘(𝐴𝑂𝐶)) = (𝐹‘(𝐵𝑂𝐶))) |
| Copyright terms: Public domain | W3C validator |