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| Mirrors > Home > MPE Home > Th. List > fveqeq2 | Structured version Visualization version GIF version | ||
| Description: Equality deduction for function value. (Contributed by BJ, 31-Aug-2022.) |
| Ref | Expression |
|---|---|
| fveqeq2 | ⊢ (𝐴 = 𝐵 → ((𝐹‘𝐴) = 𝐶 ↔ (𝐹‘𝐵) = 𝐶)) |
| Step | Hyp | Ref | Expression |
|---|---|---|---|
| 1 | id 22 | . 2 ⊢ (𝐴 = 𝐵 → 𝐴 = 𝐵) | |
| 2 | 1 | fveqeq2d 6914 | 1 ⊢ (𝐴 = 𝐵 → ((𝐹‘𝐴) = 𝐶 ↔ (𝐹‘𝐵) = 𝐶)) |
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