Theorem exdistr 1909

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 1906	. 2 |- ( E. y ( ph /\ ps ) <-> ( ph /\ E. y ps ) )
2	1	exbii 1605	1 |- ( E. x E. y ( ph /\ ps ) <-> E. x ( ph /\ E. y ps ) )

Syntax hints:   /\ wa 104   <-> wb 105   E.wex 1492

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 1447  ax-gen 1449  ax-ie1 1493  ax-ie2 1494  ax-4 1510  ax-17 1526  ax-ial 1534

This theorem depends on definitions:  df-bi 117

This theorem is referenced by:  exdistrv  1910  19.42vv  1911  3exdistr  1915  sbel2x  1998  sbexyz  2003  sbccomlem  3037  uniuni  4450  coass  5145  subhalfnqq  7409