Metamath Proof Explorer
Description: Subclass transitivity deduction. (Contributed by NM, 6-Feb-2014)
|
|
Ref |
Expression |
|
Hypotheses |
sstrid.1 |
|- A C_ B |
|
|
sstrid.2 |
|- ( ph -> B C_ C ) |
|
Assertion |
sstrid |
|- ( ph -> A C_ C ) |
Proof
| Step |
Hyp |
Ref |
Expression |
| 1 |
|
sstrid.1 |
|- A C_ B |
| 2 |
|
sstrid.2 |
|- ( ph -> B C_ C ) |
| 3 |
1
|
a1i |
|- ( ph -> A C_ B ) |
| 4 |
3 2
|
sstrd |
|- ( ph -> A C_ C ) |