Theorem exdistr 1307

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 1306	. 2 |- (E.y(ph /\ ps) <-> (ph /\ E.yps))
2	1	exbii 1049	1 |- (E.xE.y(ph /\ ps) <-> E.x(ph /\ E.yps))

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

This theorem is referenced by:  19.42vv 1308  eeanv 1321  sbel2x 1343  reeanv 1775  sbccomglem 1984  iunn0 2602  uniuni 2875  imaiun 3855

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

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