Description: Subclass transitivity deduction. (Contributed by NM, 6-Feb-2014)
Ref | Expression | ||
---|---|---|---|
Hypotheses | sstrid.1 | ⊢ 𝐴 ⊆ 𝐵 | |
sstrid.2 | ⊢ ( 𝜑 → 𝐵 ⊆ 𝐶 ) | ||
Assertion | sstrid | ⊢ ( 𝜑 → 𝐴 ⊆ 𝐶 ) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | sstrid.1 | ⊢ 𝐴 ⊆ 𝐵 | |
2 | sstrid.2 | ⊢ ( 𝜑 → 𝐵 ⊆ 𝐶 ) | |
3 | 1 | a1i | ⊢ ( 𝜑 → 𝐴 ⊆ 𝐵 ) |
4 | 3 2 | sstrd | ⊢ ( 𝜑 → 𝐴 ⊆ 𝐶 ) |