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| Mirrors > Home > MPE Home > Th. List > ssriv | Structured version Visualization version GIF version | ||
| Description: Inference based on subclass definition. (Contributed by NM, 21-Jun-1993.) |
| Ref | Expression |
|---|---|
| ssriv.1 | ⊢ (𝑥 ∈ 𝐴 → 𝑥 ∈ 𝐵) |
| Ref | Expression |
|---|---|
| ssriv | ⊢ 𝐴 ⊆ 𝐵 |
| Step | Hyp | Ref | Expression |
|---|---|---|---|
| 1 | df-ss 3968 | . 2 ⊢ (𝐴 ⊆ 𝐵 ↔ ∀𝑥(𝑥 ∈ 𝐴 → 𝑥 ∈ 𝐵)) | |
| 2 | ssriv.1 | . 2 ⊢ (𝑥 ∈ 𝐴 → 𝑥 ∈ 𝐵) | |
| 3 | 1, 2 | mpgbir 1799 | 1 ⊢ 𝐴 ⊆ 𝐵 |
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