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Theorem euan 2351
 Description: Introduction of a conjunct into uniqueness quantifier. (Contributed by NM, 19-Feb-2005.) (Proof shortened by Andrew Salmon, 9-Jul-2011.) (Proof shortened by Wolf Lammen, 24-Dec-2018.)
Hypothesis
Ref Expression
moanim.1
Assertion
Ref Expression
euan

Proof of Theorem euan
StepHypRef Expression
1 euex 2308 . . . 4
2 moanim.1 . . . . 5
3 simpl 457 . . . . 5
42, 3exlimi 1912 . . . 4
51, 4syl 16 . . 3
6 ibar 504 . . . . 5
72, 6eubid 2302 . . . 4
87biimprcd 225 . . 3
95, 8jcai 536 . 2
107biimpa 484 . 2
119, 10impbii 188 1
 Colors of variables: wff setvar class Syntax hints:  <->wb 184  /\wa 369  E.wex 1612  F/wnf 1616  E!weu 2282 This theorem is referenced by:  euanv  2355  2eu7  2385  2eu8  2386 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
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