Theorem euanv 1430

Description: Introduction of a conjunct into uniqueness quantifier.

Assertion

Ref	Expression
euanv	|- (E!x(ph /\ ps) <-> (ph /\ E!xps))

Distinct variable group:   ph,x

Proof of Theorem euanv

Step	Hyp	Ref	Expression
1		ax-17 969	. 2 |- (ph -> A.xph)
2	1	euan 1426	1 |- (E!x(ph /\ ps) <-> (ph /\ E!xps))

Syntax hints:   <-> wb 146   /\ wa 223  E!weu 1378

This theorem is referenced by:  eueq2 1914  eueq3 1915  fnopabg 3607  fvopab2 3782  fsn 3825  aceq5lem5 4719

This theorem was proved from axioms:  ax-1 4  ax-2 5  ax-3 6  ax-mp 7  ax-7 960  ax-gen 961  ax-8 962  ax-10 964  ax-11 965  ax-12 966  ax-17 969  ax-4 971  ax-5o 973  ax-6o 976  ax-9o 1121  ax-10o 1138  ax-16 1208  ax-11o 1216

This theorem depends on definitions:  df-bi 147  df-or 224  df-an 225  df-ex 979  df-sb 1170  df-eu 1380  df-mo 1381

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