Metamath Proof Explorer


Theorem sseqtri

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

Proof

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