| Metamath Proof Explorer |
< Previous
Next >
Nearby theorems |
||
| Mirrors > Home > MPE Home > Th. List > oveq2 | Structured version Visualization version GIF version | ||
| Description: Equality theorem for operation value. (Contributed by NM, 28-Feb-1995.) |
| Ref | Expression |
|---|---|
| oveq2 | ⊢ (𝐴 = 𝐵 → (𝐶𝐹𝐴) = (𝐶𝐹𝐵)) |
| Step | Hyp | Ref | Expression |
|---|---|---|---|
| 1 | opeq2 4874 | . . 3 ⊢ (𝐴 = 𝐵 → 〈𝐶, 𝐴〉 = 〈𝐶, 𝐵〉) | |
| 2 | 1 | fveq2d 6910 | . 2 ⊢ (𝐴 = 𝐵 → (𝐹‘〈𝐶, 𝐴〉) = (𝐹‘〈𝐶, 𝐵〉)) |
| 3 | df-ov 7434 | . 2 ⊢ (𝐶𝐹𝐴) = (𝐹‘〈𝐶, 𝐴〉) | |
| 4 | df-ov 7434 | . 2 ⊢ (𝐶𝐹𝐵) = (𝐹‘〈𝐶, 𝐵〉) | |
| 5 | 2, 3, 4 | 3eqtr4g 2802 | 1 ⊢ (𝐴 = 𝐵 → (𝐶𝐹𝐴) = (𝐶𝐹𝐵)) |
| Copyright terms: Public domain | W3C validator |