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Theorem euan 2261
 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 443 . . . . . 6
31, 2exlimi 1803 . . . . 5
43adantr 451 . . . 4
5 simpr 447 . . . . . 6
65eximi 1576 . . . . 5
76adantr 451 . . . 4
8 nfe1 1732 . . . . . 6
93a1d 22 . . . . . . . 8
109ancrd 537 . . . . . . 7
115, 10impbid2 195 . . . . . 6
128, 11mobid 2238 . . . . 5
1312biimpa 470 . . . 4
144, 7, 13jca32 521 . . 3
15 eu5 2242 . . 3
16 eu5 2242 . . . 4
1716anbi2i 675 . . 3
1814, 15, 173imtr4i 257 . 2
19 ibar 490 . . . 4
201, 19eubid 2211 . . 3
2120biimpa 470 . 2
2218, 21impbii 180 1
 Colors of variables: wff setvar class Syntax hints:   wb 176   wa 358  wex 1541  wnf 1544  weu 2204  wmo 2205 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1546  ax-5 1557  ax-17 1616  ax-9 1654  ax-8 1675  ax-6 1729  ax-7 1734  ax-11 1746  ax-12 1925 This theorem depends on definitions:  df-bi 177  df-or 359  df-an 360  df-tru 1319  df-ex 1542  df-nf 1545  df-sb 1649  df-eu 2208  df-mo 2209 This theorem is referenced by:  euanv  2265  2eu7  2290  2eu8  2291
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