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Metamath Proof Explorer

Theorem eqsstrrid

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

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

Proof

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