Metamath Proof Explorer

Theorem exdistr

Description: Distribution of existential quantifiers. See also exdistrv . (Contributed by NM, 9-Mar-1995)

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

Proof

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