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| Mirrors > Home > MPE Home > Th. List > imaeq1d | Structured version Visualization version GIF version | ||
| Description: Equality theorem for image. (Contributed by FL, 15-Dec-2006.) | 
| Ref | Expression | 
|---|---|
| imaeq1d.1 | ⊢ (𝜑 → 𝐴 = 𝐵) | 
| Ref | Expression | 
|---|---|
| imaeq1d | ⊢ (𝜑 → (𝐴 “ 𝐶) = (𝐵 “ 𝐶)) | 
| Step | Hyp | Ref | Expression | 
|---|---|---|---|
| 1 | imaeq1d.1 | . 2 ⊢ (𝜑 → 𝐴 = 𝐵) | |
| 2 | imaeq1 6072 | . 2 ⊢ (𝐴 = 𝐵 → (𝐴 “ 𝐶) = (𝐵 “ 𝐶)) | |
| 3 | 1, 2 | syl 17 | 1 ⊢ (𝜑 → (𝐴 “ 𝐶) = (𝐵 “ 𝐶)) | 
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