Metamath Proof Explorer
Description: Subclass transitivity deduction. (Contributed by Jonathan Ben-Naim, 3-Jun-2011)
|
|
Ref |
Expression |
|
Hypotheses |
sstrdi.1 |
|- ( ph -> A C_ B ) |
|
|
sstrdi.2 |
|- B C_ C |
|
Assertion |
sstrdi |
|- ( ph -> A C_ C ) |
Proof
| Step |
Hyp |
Ref |
Expression |
| 1 |
|
sstrdi.1 |
|- ( ph -> A C_ B ) |
| 2 |
|
sstrdi.2 |
|- B C_ C |
| 3 |
2
|
a1i |
|- ( ph -> B C_ C ) |
| 4 |
1 3
|
sstrd |
|- ( ph -> A C_ C ) |