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| Mirrors > Home > MPE Home > Th. List > elin2d | Structured version Visualization version GIF version | ||
| Description: Elementhood in the first set of an intersection - deduction version. (Contributed by Thierry Arnoux, 3-May-2020.) | 
| Ref | Expression | 
|---|---|
| elin1d.1 | ⊢ (𝜑 → 𝑋 ∈ (𝐴 ∩ 𝐵)) | 
| Ref | Expression | 
|---|---|
| elin2d | ⊢ (𝜑 → 𝑋 ∈ 𝐵) | 
| Step | Hyp | Ref | Expression | 
|---|---|---|---|
| 1 | elin1d.1 | . 2 ⊢ (𝜑 → 𝑋 ∈ (𝐴 ∩ 𝐵)) | |
| 2 | elinel2 4201 | . 2 ⊢ (𝑋 ∈ (𝐴 ∩ 𝐵) → 𝑋 ∈ 𝐵) | |
| 3 | 1, 2 | syl 17 | 1 ⊢ (𝜑 → 𝑋 ∈ 𝐵) | 
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