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Metamath Proof Explorer

Theorem eqsstrid

Description: A chained subclass and equality deduction. (Contributed by NM, 25-Apr-2004)

Ref Expression
Hypotheses eqsstrid.1 
|- A = B
eqsstrid.2 
|- ( ph -> B C_ C )
Assertion eqsstrid 
|- ( ph -> A C_ C )

Proof

Step Hyp Ref Expression
1 eqsstrid.1 
 |-  A = B
2 eqsstrid.2 
 |-  ( ph -> B C_ C )
3 1 sseq1i 
 |-  ( A C_ C <-> B C_ C )
4 2 3 sylibr 
 |-  ( ph -> A C_ C )