Theorem exdistr 1907

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 1904	. 2 |- ( E. y ( ph /\ ps ) <-> ( ph /\ E. y ps ) )
2	1	exbii 1603	1 |- ( E. x E. y ( ph /\ ps ) <-> E. x ( ph /\ E. y ps ) )

Syntax hints:   /\ wa 104   <-> wb 105   E.wex 1490

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 106  ax-ia2 107  ax-ia3 108  ax-5 1445  ax-gen 1447  ax-ie1 1491  ax-ie2 1492  ax-4 1508  ax-17 1524  ax-ial 1532

This theorem depends on definitions:  df-bi 117

This theorem is referenced by:  exdistrv  1908  19.42vv  1909  3exdistr  1913  sbel2x  1996  sbexyz  2001  sbccomlem  3035  uniuni  4445  coass  5139  subhalfnqq  7388