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| Mirrors > Home > MPE Home > Th. List > ssrab3 | Structured version Visualization version GIF version | ||
| Description: Subclass relation for a restricted class abstraction. (Contributed by Jonathan Ben-Naim, 3-Jun-2011.) |
| Ref | Expression |
|---|---|
| ssrab3.1 | ⊢ 𝐵 = {𝑥 ∈ 𝐴 ∣ 𝜑} |
| Ref | Expression |
|---|---|
| ssrab3 | ⊢ 𝐵 ⊆ 𝐴 |
| Step | Hyp | Ref | Expression |
|---|---|---|---|
| 1 | ssrab3.1 | . 2 ⊢ 𝐵 = {𝑥 ∈ 𝐴 ∣ 𝜑} | |
| 2 | ssrab2 4080 | . 2 ⊢ {𝑥 ∈ 𝐴 ∣ 𝜑} ⊆ 𝐴 | |
| 3 | 1, 2 | eqsstri 4030 | 1 ⊢ 𝐵 ⊆ 𝐴 |
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