Metamath Proof Explorer

Theorem pssssd

Description: Deduce subclass from proper subclass. (Contributed by NM, 29-Feb-1996)

Ref Expression
Hypothesis pssssd.1 
|- ( ph -> A C. B )
Assertion pssssd 
|- ( ph -> A C_ B )

Proof

Step Hyp Ref Expression
1 pssssd.1 
 |-  ( ph -> A C. B )
2 pssss 
 |-  ( A C. B -> A C_ B )
3 1 2 syl 
 |-  ( ph -> A C_ B )