Theorem euim 2344

Description: Add existential uniqueness quantifiers to an implication. Note the reversed implication in the antecedent. (Contributed by NM, 19-Oct-2005.) (Proof shortened by Andrew Salmon, 14-Jun-2011.)

Assertion

Ref	Expression
euim

Proof of Theorem euim

Step	Hyp	Ref	Expression
1		ax-1 6	. . 3
2		euimmo 2343	. . 3
3	1, 2	anim12ii 570	. 2
4		eu5 2310	. 2
5	3, 4	syl6ibr 227	1

Syntax hints:  ->wi 4  /\wa 369  A.wal 1393  E.wex 1612  E!weu 2282  E*wmo 2283

This theorem is referenced by:  2eu1  2376

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1618  ax-4 1631  ax-5 1704  ax-6 1747  ax-7 1790  ax-10 1837  ax-12 1854

This theorem depends on definitions:  df-bi 185  df-an 371  df-ex 1613  df-nf 1617  df-eu 2286  df-mo 2287