This is an inofficial mirror of http://metamath.tirix.org for personal testing of a visualizer extension only.

Metamath Proof Explorer

Theorem r19.41vv

Description: Version of r19.41v with two quantifiers. (Contributed by Thierry Arnoux, 25-Jan-2017)

Ref Expression
Assertion r19.41vv 
|- ( E. x e. A E. y e. B ( ph /\ ps ) <-> ( E. x e. A E. y e. B ph /\ ps ) )

Proof

Step Hyp Ref Expression
1 r19.41v 
 |-  ( E. y e. B ( ph /\ ps ) <-> ( E. y e. B ph /\ ps ) )
2 1 rexbii 
 |-  ( E. x e. A E. y e. B ( ph /\ ps ) <-> E. x e. A ( E. y e. B ph /\ ps ) )
3 r19.41v 
 |-  ( E. x e. A ( E. y e. B ph /\ ps ) <-> ( E. x e. A E. y e. B ph /\ ps ) )
4 2 3 bitri 
 |-  ( E. x e. A E. y e. B ( ph /\ ps ) <-> ( E. x e. A E. y e. B ph /\ ps ) )