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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 3851 | . 2 ⊢ (𝐴 ∈ (𝐵 ∖ 𝐶) ↔ (𝐴 ∈ 𝐵 ∧ ¬ 𝐴 ∈ 𝐶)) | |
2 | 1 | simprbi 500 | 1 ⊢ (𝐴 ∈ (𝐵 ∖ 𝐶) → ¬ 𝐴 ∈ 𝐶) |
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