Description: Substitution of equality into a subclass relationship. (Contributed by NM, 28-Jul-1995)
| Ref | Expression | ||
|---|---|---|---|
| Hypotheses | sseqtr.1 | |- A C_ B |
|
| sseqtr.2 | |- B = C |
||
| Assertion | sseqtri | |- A C_ C |
| Step | Hyp | Ref | Expression |
|---|---|---|---|
| 1 | sseqtr.1 | |- A C_ B |
|
| 2 | sseqtr.2 | |- B = C |
|
| 3 | 2 | sseq2i | |- ( A C_ B <-> A C_ C ) |
| 4 | 1 3 | mpbi | |- A C_ C |