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| Mirrors > Home > MPE Home > Th. List > mpteq2dva | Structured version Visualization version GIF version | ||
| Description: Slightly more general equality inference for the maps-to notation. (Contributed by Scott Fenton, 25-Apr-2012.) Remove dependency on ax-10 2141. (Revised by SN, 11-Nov-2024.) |
| Ref | Expression |
|---|---|
| mpteq2dva.1 | ⊢ ((𝜑 ∧ 𝑥 ∈ 𝐴) → 𝐵 = 𝐶) |
| Ref | Expression |
|---|---|
| mpteq2dva | ⊢ (𝜑 → (𝑥 ∈ 𝐴 ↦ 𝐵) = (𝑥 ∈ 𝐴 ↦ 𝐶)) |
| Step | Hyp | Ref | Expression |
|---|---|---|---|
| 1 | eqidd 2738 | . 2 ⊢ (𝜑 → 𝐴 = 𝐴) | |
| 2 | mpteq2dva.1 | . 2 ⊢ ((𝜑 ∧ 𝑥 ∈ 𝐴) → 𝐵 = 𝐶) | |
| 3 | 1, 2 | mpteq12dva 5231 | 1 ⊢ (𝜑 → (𝑥 ∈ 𝐴 ↦ 𝐵) = (𝑥 ∈ 𝐴 ↦ 𝐶)) |
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