Theorem exdistr2 1309

Description: Distribution of existential quantifiers.

Assertion

Ref	Expression
exdistr2	|- (E.xE.yE.z(ph /\ ps) <-> E.x(ph /\ E.yE.zps))

Distinct variable groups:   ph,y   ph,z

Proof of Theorem exdistr2

Step	Hyp	Ref	Expression
1		19.42vv 1308	. 2 |- (E.yE.z(ph /\ ps) <-> (ph /\ E.yE.zps))
2	1	exbii 1049	1 |- (E.xE.yE.z(ph /\ ps) <-> E.x(ph /\ E.yE.zps))

Syntax hints:   <-> wb 146   /\ wa 223  E.wex 978

This theorem is referenced by:  opabid 2805

This theorem was proved from axioms:  ax-1 4  ax-2 5  ax-3 6  ax-mp 7  ax-gen 961  ax-17 969  ax-4 971  ax-5o 973  ax-6o 976

This theorem depends on definitions:  df-bi 147  df-or 224  df-an 225  df-ex 979

Copyright terms: Public domain