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Metamath Proof Explorer

Theorem 3sstr3g

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

Ref Expression
Hypotheses 3sstr3g.1 
|- ( ph -> A C_ B )
3sstr3g.2 
|- A = C
3sstr3g.3 
|- B = D
Assertion 3sstr3g 
|- ( ph -> C C_ D )

Proof

Step Hyp Ref Expression
1 3sstr3g.1 
 |-  ( ph -> A C_ B )
2 3sstr3g.2 
 |-  A = C
3 3sstr3g.3 
 |-  B = D
4 2 1 eqsstrrid 
 |-  ( ph -> C C_ B )
5 4 3 sseqtrdi 
 |-  ( ph -> C C_ D )