Theorem bj-eeanvw

Description: Version of exdistrv with a disjoint variable condition on x , y not requiring ax-11 . (The same can be done with eeeanv and ee4anv .) (Contributed by BJ, 29-Sep-2019) (Proof modification is discouraged.)

	Ref	Expression
Assertion	bj-eeanvw	|- ( 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 ) )
3		19.41v	|- ( E. x ( ph /\ E. y ps ) <-> ( E. x ph /\ E. y ps ) )
4	2 3	bitri	|- ( E. x E. y ( ph /\ ps ) <-> ( E. x ph /\ E. y ps ) )