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| Mirrors > Home > MPE Home > Th. List > ssdifssd | Structured version Visualization version GIF version | ||
| Description: If 𝐴 is contained in 𝐵, then (𝐴 ∖ 𝐶) is also contained in 𝐵. Deduction form of ssdifss 4140. (Contributed by David Moews, 1-May-2017.) |
| Ref | Expression |
|---|---|
| ssdifd.1 | ⊢ (𝜑 → 𝐴 ⊆ 𝐵) |
| Ref | Expression |
|---|---|
| ssdifssd | ⊢ (𝜑 → (𝐴 ∖ 𝐶) ⊆ 𝐵) |
| Step | Hyp | Ref | Expression |
|---|---|---|---|
| 1 | ssdifd.1 | . 2 ⊢ (𝜑 → 𝐴 ⊆ 𝐵) | |
| 2 | ssdifss 4140 | . 2 ⊢ (𝐴 ⊆ 𝐵 → (𝐴 ∖ 𝐶) ⊆ 𝐵) | |
| 3 | 1, 2 | syl 17 | 1 ⊢ (𝜑 → (𝐴 ∖ 𝐶) ⊆ 𝐵) |
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