Metamath Proof Explorer |
< Previous
Next >
Nearby theorems |
||
Mirrors > Home > MPE Home > Th. List > resmptd | Structured version Visualization version GIF version |
Description: Restriction of the mapping operation, deduction form. (Contributed by Glauco Siliprandi, 11-Dec-2019.) |
Ref | Expression |
---|---|
resmptd.b | ⊢ (𝜑 → 𝐵 ⊆ 𝐴) |
Ref | Expression |
---|---|
resmptd | ⊢ (𝜑 → ((𝑥 ∈ 𝐴 ↦ 𝐶) ↾ 𝐵) = (𝑥 ∈ 𝐵 ↦ 𝐶)) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | resmptd.b | . 2 ⊢ (𝜑 → 𝐵 ⊆ 𝐴) | |
2 | resmpt 5879 | . 2 ⊢ (𝐵 ⊆ 𝐴 → ((𝑥 ∈ 𝐴 ↦ 𝐶) ↾ 𝐵) = (𝑥 ∈ 𝐵 ↦ 𝐶)) | |
3 | 1, 2 | syl 17 | 1 ⊢ (𝜑 → ((𝑥 ∈ 𝐴 ↦ 𝐶) ↾ 𝐵) = (𝑥 ∈ 𝐵 ↦ 𝐶)) |
Copyright terms: Public domain | W3C validator |