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Metamath Proof Explorer

Theorem 3sstr3d

Description: Substitution of equality into both sides of a subclass relationship. (Contributed by NM, 1-Oct-2000)

Ref Expression
Hypotheses 3sstr3d.1 
|- ( ph -> A C_ B )
3sstr3d.2 
|- ( ph -> A = C )
3sstr3d.3 
|- ( ph -> B = D )
Assertion 3sstr3d 
|- ( ph -> C C_ D )

Proof

Step Hyp Ref Expression
1 3sstr3d.1 
 |-  ( ph -> A C_ B )
2 3sstr3d.2 
 |-  ( ph -> A = C )
3 3sstr3d.3 
 |-  ( ph -> B = D )
4 2 1 eqsstrrd 
 |-  ( ph -> C C_ B )
5 4 3 sseqtrd 
 |-  ( ph -> C C_ D )