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| Mirrors > Home > MPE Home > Th. List > eldifn | Structured version Visualization version GIF version | ||
| Description: Implication of membership in a class difference. (Contributed by NM, 3-May-1994.) |
| Ref | Expression |
|---|---|
| eldifn | ⊢ (𝐴 ∈ (𝐵 ∖ 𝐶) → ¬ 𝐴 ∈ 𝐶) |
| Step | Hyp | Ref | Expression |
|---|---|---|---|
| 1 | eldif 3961 | . 2 ⊢ (𝐴 ∈ (𝐵 ∖ 𝐶) ↔ (𝐴 ∈ 𝐵 ∧ ¬ 𝐴 ∈ 𝐶)) | |
| 2 | 1 | simprbi 496 | 1 ⊢ (𝐴 ∈ (𝐵 ∖ 𝐶) → ¬ 𝐴 ∈ 𝐶) |
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