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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 4010 | . 2 ⊢ {𝑥 ∈ 𝐴 ∣ 𝜑} ⊆ 𝐴 | |
3 | 1, 2 | eqsstri 3952 | 1 ⊢ 𝐵 ⊆ 𝐴 |
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