Metamath Proof Explorer

Theorem bnj1405

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

Ref Expression
Hypothesis bnj1405.1 
|- ( ph -> X e. U_ y e. A B )
Assertion bnj1405 
|- ( ph -> E. y e. A X e. B )

Proof

Step Hyp Ref Expression
1 bnj1405.1 
 |-  ( ph -> X e. U_ y e. A B )
2 eliun 
 |-  ( X e. U_ y e. A B <-> E. y e. A X e. B )
3 1 2 sylib 
 |-  ( ph -> E. y e. A X e. B )