Metamath Proof Explorer

Theorem 19.42vv

Description: Version of 19.42 with two quantifiers and a disjoint variable condition requiring fewer axioms. (Contributed by NM, 16-Mar-1995)

Ref Expression
Assertion 19.42vv 
|- ( E. x E. y ( ph /\ ps ) <-> ( ph /\ E. x E. y ps ) )

Proof

Step Hyp Ref Expression
1 exdistr 
 |-  ( E. x E. y ( ph /\ ps ) <-> E. x ( ph /\ E. y ps ) )
2 19.42v 
 |-  ( E. x ( ph /\ E. y ps ) <-> ( ph /\ E. x E. y ps ) )
3 1 2 bitri 
 |-  ( E. x E. y ( ph /\ ps ) <-> ( ph /\ E. x E. y ps ) )