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| Mirrors > Home > MPE Home > Th. List > oveq12d | Structured version Visualization version GIF version | ||
| Description: Equality deduction for operation value. (Contributed by NM, 13-Mar-1995.) (Proof shortened by Andrew Salmon, 22-Oct-2011.) |
| Ref | Expression |
|---|---|
| oveq1d.1 | ⊢ (𝜑 → 𝐴 = 𝐵) |
| oveq12d.2 | ⊢ (𝜑 → 𝐶 = 𝐷) |
| Ref | Expression |
|---|---|
| oveq12d | ⊢ (𝜑 → (𝐴𝐹𝐶) = (𝐵𝐹𝐷)) |
| Step | Hyp | Ref | Expression |
|---|---|---|---|
| 1 | oveq1d.1 | . 2 ⊢ (𝜑 → 𝐴 = 𝐵) | |
| 2 | oveq12d.2 | . 2 ⊢ (𝜑 → 𝐶 = 𝐷) | |
| 3 | oveq12 7440 | . 2 ⊢ ((𝐴 = 𝐵 ∧ 𝐶 = 𝐷) → (𝐴𝐹𝐶) = (𝐵𝐹𝐷)) | |
| 4 | 1, 2, 3 | syl2anc 584 | 1 ⊢ (𝜑 → (𝐴𝐹𝐶) = (𝐵𝐹𝐷)) |
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