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Metamath Proof Explorer

Theorem sseqtrdi

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

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

Proof

Step Hyp Ref Expression
1 sseqtrdi.1 
 |-  ( ph -> A C_ B )
2 sseqtrdi.2 
 |-  B = C
3 2 sseq2i 
 |-  ( A C_ B <-> A C_ C )
4 1 3 sylib 
 |-  ( ph -> A C_ C )