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Theorem euan 2345
 Description: Introduction of a conjunct into uniqueness quantifier. (Contributed by NM, 19-Feb-2005.) (Proof shortened by Andrew Salmon, 9-Jul-2011.)
Hypothesis
Ref Expression
moanim.1
Assertion
Ref Expression
euan

Proof of Theorem euan
StepHypRef Expression
1 moanim.1 . . . . . 6
2 simpl 445 . . . . . 6
31, 2exlimi 1824 . . . . 5
43adantr 453 . . . 4
5 exsimpr 1604 . . . . 5
65adantr 453 . . . 4
7 nfe1 1750 . . . . . 6
8 simpr 449 . . . . . . 7
93a1d 24 . . . . . . . 8
109ancrd 539 . . . . . . 7
118, 10impbid2 197 . . . . . 6
127, 11mobid 2322 . . . . 5
1312biimpa 472 . . . 4
144, 6, 13jca32 523 . . 3
15 eu5 2326 . . 3
16 eu5 2326 . . . 4
1716anbi2i 677 . . 3
1814, 15, 173imtr4i 259 . 2
19 ibar 492 . . . 4
201, 19eubid 2295 . . 3
2120biimpa 472 . 2
2218, 21impbii 182 1
 Colors of variables: wff set class Syntax hints:   wb 178   wa 360  wex 1551  wnf 1554  weu 2288  wmo 2289 This theorem is referenced by:  euanv  2349  2eu7  2374  2eu8  2375 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1556  ax-5 1567  ax-17 1628  ax-9 1669  ax-8 1690  ax-6 1747  ax-7 1752  ax-11 1764  ax-12 1954 This theorem depends on definitions:  df-bi 179  df-or 361  df-an 362  df-tru 1329  df-ex 1552  df-nf 1555  df-sb 1661  df-eu 2292  df-mo 2293
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