Intuitionistic Logic Explorer < Previous   Next > Nearby theorems Mirrors  >  Home  >  ILE Home  >  Th. List  >  2euex Unicode version

Theorem 2euex 2029
 Description: Double quantification with existential uniqueness. (Contributed by NM, 3-Dec-2001.) (Proof shortened by Andrew Salmon, 9-Jul-2011.)
Assertion
Ref Expression
2euex

Proof of Theorem 2euex
StepHypRef Expression
1 eu5 1989 . 2
2 excom 1595 . . . 4
3 hbe1 1425 . . . . . 6
43hbmo 1981 . . . . 5
5 19.8a 1523 . . . . . . 7
65moimi 2007 . . . . . 6
7 df-mo 1946 . . . . . 6
86, 7sylib 120 . . . . 5
94, 8eximdh 1543 . . . 4
102, 9syl5bi 150 . . 3
1110impcom 123 . 2
121, 11sylbi 119 1
 Colors of variables: wff set class Syntax hints:   wi 4   wa 102  wex 1422  weu 1942  wmo 1943 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 104  ax-ia2 105  ax-ia3 106  ax-io 663  ax-5 1377  ax-7 1378  ax-gen 1379  ax-ie1 1423  ax-ie2 1424  ax-8 1436  ax-10 1437  ax-11 1438  ax-i12 1439  ax-bndl 1440  ax-4 1441  ax-17 1460  ax-i9 1464  ax-ial 1468  ax-i5r 1469 This theorem depends on definitions:  df-bi 115  df-tru 1288  df-nf 1391  df-sb 1687  df-eu 1945  df-mo 1946 This theorem is referenced by: (None)
 Copyright terms: Public domain W3C validator