Theorem exdistr 1902

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 1899	. 2 |- ( E. y ( ph /\ ps ) <-> ( ph /\ E. y ps ) )
2	1	exbii 1598	1 |- ( E. x E. y ( ph /\ ps ) <-> E. x ( ph /\ E. y ps ) )

Syntax hints:   /\ wa 103   <-> wb 104   E.wex 1485

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 105  ax-ia2 106  ax-ia3 107  ax-5 1440  ax-gen 1442  ax-ie1 1486  ax-ie2 1487  ax-4 1503  ax-17 1519  ax-ial 1527

This theorem depends on definitions:  df-bi 116

This theorem is referenced by:  exdistrv  1903  19.42vv  1904  3exdistr  1908  sbel2x  1991  sbexyz  1996  sbccomlem  3029  uniuni  4436  coass  5129  subhalfnqq  7376