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Metamath Proof Explorer

Theorem sselpwd

Description: Elementhood to a power set. (Contributed by Thierry Arnoux, 18-May-2020)

Ref Expression
Hypotheses sselpwd.1 
|- ( ph -> B e. V )
sselpwd.2 
|- ( ph -> A C_ B )
Assertion sselpwd 
|- ( ph -> A e. ~P B )

Proof

Step Hyp Ref Expression
1 sselpwd.1 
 |-  ( ph -> B e. V )
2 sselpwd.2 
 |-  ( ph -> A C_ B )
3 1 2 ssexd 
 |-  ( ph -> A e. _V )
4 3 2 elpwd 
 |-  ( ph -> A e. ~P B )