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Mirrors > Home > MPE Home > Th. List > inss2 | Structured version Visualization version GIF version |
Description: The intersection of two classes is a subset of one of them. Part of Exercise 12 of [TakeutiZaring] p. 18. (Contributed by NM, 27-Apr-1994.) |
Ref | Expression |
---|---|
inss2 | ⊢ (𝐴 ∩ 𝐵) ⊆ 𝐵 |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | incom 3767 | . 2 ⊢ (𝐵 ∩ 𝐴) = (𝐴 ∩ 𝐵) | |
2 | inss1 3795 | . 2 ⊢ (𝐵 ∩ 𝐴) ⊆ 𝐵 | |
3 | 1, 2 | eqsstr3i 3599 | 1 ⊢ (𝐴 ∩ 𝐵) ⊆ 𝐵 |
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