Theorem euanv 1471

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 1007	. 2 |- (ph -> A.xph)
2	1	euan 1467	1 |- (E!x(ph /\ ps) <-> (ph /\ E!xps))

Syntax hints:   <-> wb 144   /\ wa 221  E!weu 1419

This theorem is referenced by:  eueq2 1964  eueq3 1965  fnopabg 3722  fvopab2 3902  fsn 3948  aceq5lem5 4885

This theorem was proved from axioms:  ax-1 4  ax-2 5  ax-3 6  ax-mp 7  ax-7 998  ax-gen 999  ax-8 1000  ax-10 1002  ax-11 1003  ax-12 1004  ax-17 1007  ax-4 1009  ax-5o 1011  ax-6o 1014  ax-9o 1159  ax-10o 1177  ax-16 1247  ax-11o 1255

This theorem depends on definitions:  df-bi 145  df-or 222  df-an 223  df-ex 1017  df-sb 1209  df-eu 1421  df-mo 1422

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