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| Mirrors > Home > MPE Home > Th. List > sselda | Structured version Visualization version GIF version | ||
| Description: Membership deduction from subclass relationship. (Contributed by NM, 26-Jun-2014.) |
| Ref | Expression |
|---|---|
| sseld.1 | ⊢ (𝜑 → 𝐴 ⊆ 𝐵) |
| Ref | Expression |
|---|---|
| sselda | ⊢ ((𝜑 ∧ 𝐶 ∈ 𝐴) → 𝐶 ∈ 𝐵) |
| Step | Hyp | Ref | Expression |
|---|---|---|---|
| 1 | sseld.1 | . . 3 ⊢ (𝜑 → 𝐴 ⊆ 𝐵) | |
| 2 | 1 | sseld 3982 | . 2 ⊢ (𝜑 → (𝐶 ∈ 𝐴 → 𝐶 ∈ 𝐵)) |
| 3 | 2 | imp 406 | 1 ⊢ ((𝜑 ∧ 𝐶 ∈ 𝐴) → 𝐶 ∈ 𝐵) |
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