| Metamath Proof Explorer |
< Previous
Next >
Nearby theorems |
||
| Mirrors > Home > MPE Home > Th. List > ssexd | Structured version Visualization version GIF version | ||
| Description: A subclass of a set is a set. Deduction form of ssexg 5323. (Contributed by David Moews, 1-May-2017.) |
| Ref | Expression |
|---|---|
| ssexd.1 | ⊢ (𝜑 → 𝐵 ∈ 𝐶) |
| ssexd.2 | ⊢ (𝜑 → 𝐴 ⊆ 𝐵) |
| Ref | Expression |
|---|---|
| ssexd | ⊢ (𝜑 → 𝐴 ∈ V) |
| Step | Hyp | Ref | Expression |
|---|---|---|---|
| 1 | ssexd.2 | . 2 ⊢ (𝜑 → 𝐴 ⊆ 𝐵) | |
| 2 | ssexd.1 | . 2 ⊢ (𝜑 → 𝐵 ∈ 𝐶) | |
| 3 | ssexg 5323 | . 2 ⊢ ((𝐴 ⊆ 𝐵 ∧ 𝐵 ∈ 𝐶) → 𝐴 ∈ V) | |
| 4 | 1, 2, 3 | syl2anc 584 | 1 ⊢ (𝜑 → 𝐴 ∈ V) |
| Copyright terms: Public domain | W3C validator |