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Theorem 2euex 2360
 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 2326 . 2
2 excom 1759 . . . 4
3 nfe1 1750 . . . . . 6
43nfmo 2305 . . . . 5
5 19.8a 1765 . . . . . . 7
65moimi 2335 . . . . . 6
7 df-mo 2293 . . . . . 6
86, 7sylib 190 . . . . 5
94, 8eximd 1789 . . . 4
102, 9syl5bi 210 . . 3
1110impcom 421 . 2
121, 11sylbi 189 1
 Colors of variables: wff set class Syntax hints:   wi 4   wa 360  wex 1551  weu 2288  wmo 2289 This theorem is referenced by:  2exeu  2365 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1556  ax-5 1567  ax-17 1628  ax-9 1669  ax-8 1690  ax-6 1747  ax-7 1752  ax-11 1764  ax-12 1954 This theorem depends on definitions:  df-bi 179  df-or 361  df-an 362  df-tru 1329  df-ex 1552  df-nf 1555  df-sb 1661  df-eu 2292  df-mo 2293
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