Metamath Proof Explorer

Theorem exdistr2

Description: Distribution of existential quantifiers. (Contributed by NM, 17-Mar-1995)

Ref Expression
Assertion exdistr2 
|- ( E. x E. y E. z ( ph /\ ps ) <-> E. x ( ph /\ E. y E. z ps ) )

Proof

Step Hyp Ref Expression
1 19.42vv 
 |-  ( E. y E. z ( ph /\ ps ) <-> ( ph /\ E. y E. z ps ) )
2 1 exbii 
 |-  ( E. x E. y E. z ( ph /\ ps ) <-> E. x ( ph /\ E. y E. z ps ) )