Description: A subclass transitivity deduction. (Contributed by NM, 27-Sep-2004)
Ref | Expression | ||
---|---|---|---|
Hypotheses | sylan9ssr.1 | |- ( ph -> A C_ B ) |
|
sylan9ssr.2 | |- ( ps -> B C_ C ) |
||
Assertion | sylan9ssr | |- ( ( ps /\ ph ) -> A C_ C ) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | sylan9ssr.1 | |- ( ph -> A C_ B ) |
|
2 | sylan9ssr.2 | |- ( ps -> B C_ C ) |
|
3 | 1 2 | sylan9ss | |- ( ( ph /\ ps ) -> A C_ C ) |
4 | 3 | ancoms | |- ( ( ps /\ ph ) -> A C_ C ) |