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Theorem euan 1972
 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
euan.1
Assertion
Ref Expression
euan

Proof of Theorem euan
StepHypRef Expression
1 euan.1 . . . . . 6
2 simpl 106 . . . . . 6
31, 2exlimih 1500 . . . . 5
43adantr 265 . . . 4
5 simpr 107 . . . . . 6
65eximi 1507 . . . . 5
76adantr 265 . . . 4
8 hbe1 1400 . . . . . 6
93a1d 22 . . . . . . . 8
109ancrd 313 . . . . . . 7
115, 10impbid2 135 . . . . . 6
128, 11mobidh 1950 . . . . 5
1312biimpa 284 . . . 4
144, 7, 13jca32 297 . . 3
15 eu5 1963 . . 3
16 eu5 1963 . . . 4
1716anbi2i 438 . . 3
1814, 15, 173imtr4i 194 . 2
19 ibar 289 . . . 4
201, 19eubidh 1922 . . 3
2120biimpa 284 . 2
2218, 21impbii 121 1
 Colors of variables: wff set class Syntax hints:   wi 4   wa 101   wb 102  wal 1257  wex 1397  weu 1916  wmo 1917 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 103  ax-ia2 104  ax-ia3 105  ax-io 640  ax-5 1352  ax-7 1353  ax-gen 1354  ax-ie1 1398  ax-ie2 1399  ax-8 1411  ax-10 1412  ax-11 1413  ax-i12 1414  ax-bndl 1415  ax-4 1416  ax-17 1435  ax-i9 1439  ax-ial 1443  ax-i5r 1444 This theorem depends on definitions:  df-bi 114  df-nf 1366  df-sb 1662  df-eu 1919  df-mo 1920 This theorem is referenced by:  euanv  1973  2eu7  2010
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