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Theorem 2euex 2366
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 2310 . 2
2 excom 1849 . . . 4
3 nfe1 1840 . . . . . 6
43nfmo 2301 . . . . 5
5 19.8a 1857 . . . . . . 7
65moimi 2340 . . . . . 6
7 df-mo 2287 . . . . . 6
86, 7sylib 196 . . . . 5
94, 8eximd 1882 . . . 4
102, 9syl5bi 217 . . 3
1110impcom 430 . 2
121, 11sylbi 195 1
Colors of variables: wff setvar class
Syntax hints:  ->wi 4  /\wa 369  E.wex 1612  E!weu 2282  E*wmo 2283
This theorem is referenced by:  2exeu  2371
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1618  ax-4 1631  ax-5 1704  ax-6 1747  ax-7 1790  ax-10 1837  ax-11 1842  ax-12 1854  ax-13 1999
This theorem depends on definitions:  df-bi 185  df-an 371  df-tru 1398  df-ex 1613  df-nf 1617  df-eu 2286  df-mo 2287
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