Description: Subclass transitivity deduction. (Contributed by Jonathan Ben-Naim, 3-Jun-2011)
Ref | Expression | ||
---|---|---|---|
Hypotheses | sseqtrid.1 | ⊢ 𝐵 ⊆ 𝐴 | |
sseqtrid.2 | ⊢ ( 𝜑 → 𝐴 = 𝐶 ) | ||
Assertion | sseqtrid | ⊢ ( 𝜑 → 𝐵 ⊆ 𝐶 ) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | sseqtrid.1 | ⊢ 𝐵 ⊆ 𝐴 | |
2 | sseqtrid.2 | ⊢ ( 𝜑 → 𝐴 = 𝐶 ) | |
3 | 1 | a1i | ⊢ ( 𝜑 → 𝐵 ⊆ 𝐴 ) |
4 | 3 2 | sseqtrd | ⊢ ( 𝜑 → 𝐵 ⊆ 𝐶 ) |