Theorem euanv 1425

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-17 968	. 2 |- (ph -> A.xph)
2	1	euan 1421	1 |- (E!x(ph /\ ps) <-> (ph /\ E!xps))

Syntax hints:   <-> wb 146   /\ wa 223  E!weu 1373

This theorem is referenced by:  eueq2 1909  eueq3 1910  fnopabg 3601  fvopab2 3776  fsn 3819  aceq5lem5 4711

This theorem was proved from axioms:  ax-1 4  ax-2 5  ax-3 6  ax-mp 7  ax-7 959  ax-gen 960  ax-8 961  ax-10 963  ax-11 964  ax-12 965  ax-17 968  ax-4 970  ax-5o 972  ax-6o 975  ax-9o 1119  ax-10o 1136  ax-16 1206  ax-11o 1213

This theorem depends on definitions:  df-bi 147  df-or 224  df-an 225  df-ex 978  df-sb 1168  df-eu 1375  df-mo 1376

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