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| Mirrors > Home > MPE Home > Th. List > mpteq2dv | Structured version Visualization version GIF version | ||
| Description: An equality inference for the maps-to notation. (Contributed by Mario Carneiro, 23-Aug-2014.) |
| Ref | Expression |
|---|---|
| mpteq2dv.1 | ⊢ (𝜑 → 𝐵 = 𝐶) |
| Ref | Expression |
|---|---|
| mpteq2dv | ⊢ (𝜑 → (𝑥 ∈ 𝐴 ↦ 𝐵) = (𝑥 ∈ 𝐴 ↦ 𝐶)) |
| Step | Hyp | Ref | Expression |
|---|---|---|---|
| 1 | mpteq2dv.1 | . . 3 ⊢ (𝜑 → 𝐵 = 𝐶) | |
| 2 | 1 | adantr 480 | . 2 ⊢ ((𝜑 ∧ 𝑥 ∈ 𝐴) → 𝐵 = 𝐶) |
| 3 | 2 | mpteq2dva 5242 | 1 ⊢ (𝜑 → (𝑥 ∈ 𝐴 ↦ 𝐵) = (𝑥 ∈ 𝐴 ↦ 𝐶)) |
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