Metamath Proof Explorer

Theorem bnj1361

Description: First-order logic and set theory. (Contributed by Jonathan Ben-Naim, 3-Jun-2011) (New usage is discouraged.)

Ref Expression
Hypothesis bnj1361.1 
|- ( ph -> A. x ( x e. A -> x e. B ) )
Assertion bnj1361 
|- ( ph -> A C_ B )

Proof

Step Hyp Ref Expression
1 bnj1361.1 
 |-  ( ph -> A. x ( x e. A -> x e. B ) )
2 df-ss 
 |-  ( A C_ B <-> A. x ( x e. A -> x e. B ) )
3 1 2 sylibr 
 |-  ( ph -> A C_ B )