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| Mirrors > Home > MPE Home > Th. List > difexg | Structured version Visualization version GIF version | ||
| Description: Existence of a difference. (Contributed by NM, 26-May-1998.) |
| Ref | Expression |
|---|---|
| difexg | ⊢ (𝐴 ∈ 𝑉 → (𝐴 ∖ 𝐵) ∈ V) |
| Step | Hyp | Ref | Expression |
|---|---|---|---|
| 1 | difss 4136 | . 2 ⊢ (𝐴 ∖ 𝐵) ⊆ 𝐴 | |
| 2 | ssexg 5323 | . 2 ⊢ (((𝐴 ∖ 𝐵) ⊆ 𝐴 ∧ 𝐴 ∈ 𝑉) → (𝐴 ∖ 𝐵) ∈ V) | |
| 3 | 1, 2 | mpan 690 | 1 ⊢ (𝐴 ∈ 𝑉 → (𝐴 ∖ 𝐵) ∈ V) |
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