Theorem bj-eeanvw 32704

Description: Version of eeanv 2182 with a DV condition on x , y not requiring ax-11 2034. (The same can be done with eeeanv 2183 and ee4anv 2184.) (Contributed by BJ, 29-Sep-2019.) (Proof modification is discouraged.)

Assertion

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

Distinct variable groups:   ph, y   ps, x   x, y

Allowed substitution hints:   ph( x)   ps( y)

Proof of Theorem bj-eeanvw

Step	Hyp	Ref	Expression
1		19.42v 1918	. . 3 |- ( E. y ( ph /\ ps ) <-> ( ph /\ E. y ps ) )
2	1	exbii 1774	. 2 |- ( E. x E. y ( ph /\ ps ) <-> E. x ( ph /\ E. y ps ) )
3		19.41v 1914	. 2 |- ( E. x ( ph /\ E. y ps ) <-> ( E. x ph /\ E. y ps ) )
4	2, 3	bitri 264	1 |- ( E. x E. y ( ph /\ ps ) <-> ( E. x ph /\ E. y ps ) )

Syntax hints:   <-> wb 196   /\ wa 384   E.wex 1704

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1722  ax-4 1737  ax-5 1839  ax-6 1888

This theorem depends on definitions:  df-bi 197  df-an 386  df-ex 1705

This theorem is referenced by: (None)