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| Mirrors > Home > MPE Home > Th. List > inss1 | Structured version Visualization version GIF version | ||
| Description: The intersection of two classes is a subset of one of them. Part of Exercise 12 of [TakeutiZaring] p. 18. (Contributed by NM, 27-Apr-1994.) |
| Ref | Expression |
|---|---|
| inss1 | ⊢ (𝐴 ∩ 𝐵) ⊆ 𝐴 |
| Step | Hyp | Ref | Expression |
|---|---|---|---|
| 1 | elinel1 4201 | . 2 ⊢ (𝑥 ∈ (𝐴 ∩ 𝐵) → 𝑥 ∈ 𝐴) | |
| 2 | 1 | ssriv 3987 | 1 ⊢ (𝐴 ∩ 𝐵) ⊆ 𝐴 |
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