Theorem exdistr 1309

Description: Distribution of existential quantifiers.

Assertion

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

Distinct variable group:   ph,y

Proof of Theorem exdistr

Step	Hyp	Ref	Expression
1		19.42v 1308	. 2 |- (E.y(ph /\ ps) <-> (ph /\ E.yps))
2	1	exbii 1051	1 |- (E.xE.y(ph /\ ps) <-> E.x(ph /\ E.yps))

Syntax hints:   <-> wb 146   /\ wa 223  E.wex 980

This theorem is referenced by:  19.42vv 1310  eeanv 1323  sbel2x 1345  reeanv 1778  sbccomglem 1988  iunn0 2607  uniuni 2880  imaiun 3864

This theorem was proved from axioms:  ax-1 4  ax-2 5  ax-3 6  ax-mp 7  ax-gen 963  ax-17 971  ax-4 973  ax-5o 975  ax-6o 978

This theorem depends on definitions:  df-bi 147  df-or 224  df-an 225  df-ex 981

Copyright terms: Public domain