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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 4761 | . . 3 ⊢ (𝐴 = 𝐵 → 〈𝐶, 𝐴〉 = 〈𝐶, 𝐵〉) | |
2 | 1 | fveq2d 6678 | . 2 ⊢ (𝐴 = 𝐵 → (𝐹‘〈𝐶, 𝐴〉) = (𝐹‘〈𝐶, 𝐵〉)) |
3 | df-ov 7173 | . 2 ⊢ (𝐶𝐹𝐴) = (𝐹‘〈𝐶, 𝐴〉) | |
4 | df-ov 7173 | . 2 ⊢ (𝐶𝐹𝐵) = (𝐹‘〈𝐶, 𝐵〉) | |
5 | 2, 3, 4 | 3eqtr4g 2798 | 1 ⊢ (𝐴 = 𝐵 → (𝐶𝐹𝐴) = (𝐶𝐹𝐵)) |
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