Theorem exdistr 1828

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

Assertion

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

Distinct variable group:   ph, y

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

Proof of Theorem exdistr

Step	Hyp	Ref	Expression
1		19.42v 1827	. 2 |- ( E. y ( ph /\ ps ) <-> ( ph /\ E. y ps ) )
2	1	exbii 1536	1 |- ( E. x E. y ( ph /\ ps ) <-> E. x ( ph /\ E. y ps ) )

Syntax hints:   /\ wa 102   <-> wb 103   E.wex 1421

This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 104  ax-ia2 105  ax-ia3 106  ax-5 1376  ax-gen 1378  ax-ie1 1422  ax-ie2 1423  ax-4 1440  ax-17 1459  ax-ial 1467

This theorem depends on definitions:  df-bi 115

This theorem is referenced by:  19.42vv  1829  3exdistr  1833  sbel2x  1915  sbexyz  1920  sbccomlem  2888  uniuni  4201  coass  4859  subhalfnqq  6604