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Theorem euan 1953
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 102 . . . . . 6
31, 2exlimih 1481 . . . . 5
43adantr 261 . . . 4
5 simpr 103 . . . . . 6
65eximi 1488 . . . . 5
76adantr 261 . . . 4
8 hbe1 1381 . . . . . 6
93a1d 22 . . . . . . . 8
109ancrd 309 . . . . . . 7
115, 10impbid2 131 . . . . . 6
128, 11mobidh 1931 . . . . 5
1312biimpa 280 . . . 4
144, 7, 13jca32 293 . . 3
15 eu5 1944 . . 3
16 eu5 1944 . . . 4
1716anbi2i 430 . . 3
1814, 15, 173imtr4i 190 . 2
19 ibar 285 . . . 4
201, 19eubidh 1903 . . 3
2120biimpa 280 . 2
2218, 21impbii 117 1
Colors of variables: wff set class
Syntax hints:   wi 4   wa 97   wb 98  wal 1240  wex 1378  weu 1897  wmo 1898
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 99  ax-ia2 100  ax-ia3 101  ax-io 629  ax-5 1333  ax-7 1334  ax-gen 1335  ax-ie1 1379  ax-ie2 1380  ax-8 1392  ax-10 1393  ax-11 1394  ax-i12 1395  ax-bnd 1396  ax-4 1397  ax-17 1416  ax-i9 1420  ax-ial 1424  ax-i5r 1425
This theorem depends on definitions:  df-bi 110  df-nf 1347  df-sb 1643  df-eu 1900  df-mo 1901
This theorem is referenced by:  euanv  1954  2eu7  1991
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