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Mirrors > Home > ILE Home > Th. List > oveq2 | 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 3541 | . . 3 ⊢ (A = B → 〈𝐶, A〉 = 〈𝐶, B〉) | |
2 | 1 | fveq2d 5125 | . 2 ⊢ (A = B → (𝐹‘〈𝐶, A〉) = (𝐹‘〈𝐶, B〉)) |
3 | df-ov 5458 | . 2 ⊢ (𝐶𝐹A) = (𝐹‘〈𝐶, A〉) | |
4 | df-ov 5458 | . 2 ⊢ (𝐶𝐹B) = (𝐹‘〈𝐶, B〉) | |
5 | 2, 3, 4 | 3eqtr4g 2094 | 1 ⊢ (A = B → (𝐶𝐹A) = (𝐶𝐹B)) |
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