Theorem exdistr2 1311

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 1310	. 2 |- (E.yE.z(ph /\ ps) <-> (ph /\ E.yE.zps))
2	1	exbii 1051	1 |- (E.xE.yE.z(ph /\ ps) <-> E.x(ph /\ E.yE.zps))

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

This theorem is referenced by:  opabid 2810

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

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