Description: Subclass transitivity inference. (Contributed by NM, 5-May-2000)
Ref | Expression | ||
---|---|---|---|
Hypotheses | sstri.1 | ⊢ 𝐴 ⊆ 𝐵 | |
sstri.2 | ⊢ 𝐵 ⊆ 𝐶 | ||
Assertion | sstri | ⊢ 𝐴 ⊆ 𝐶 |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | sstri.1 | ⊢ 𝐴 ⊆ 𝐵 | |
2 | sstri.2 | ⊢ 𝐵 ⊆ 𝐶 | |
3 | sstr2 | ⊢ ( 𝐴 ⊆ 𝐵 → ( 𝐵 ⊆ 𝐶 → 𝐴 ⊆ 𝐶 ) ) | |
4 | 1 2 3 | mp2 | ⊢ 𝐴 ⊆ 𝐶 |