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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 7222 | . 2 ⊢ ((𝐴 = 𝐵 ∧ 𝐶 = 𝐷) → (𝐴𝐹𝐶) = (𝐵𝐹𝐷)) | |
4 | 1, 2, 3 | syl2anc 587 | 1 ⊢ (𝜑 → (𝐴𝐹𝐶) = (𝐵𝐹𝐷)) |
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