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Theorem 2euex 2276
 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 2242 . 2
2 excom 1741 . . . 4
3 nfe1 1732 . . . . . 6
43nfmo 2221 . . . . 5
5 19.8a 1756 . . . . . . 7
65moimi 2251 . . . . . 6
7 df-mo 2209 . . . . . 6
86, 7sylib 188 . . . . 5
94, 8eximd 1770 . . . 4
102, 9syl5bi 208 . . 3
1110impcom 419 . 2
121, 11sylbi 187 1
 Colors of variables: wff setvar class Syntax hints:   wi 4   wa 358  wex 1541  weu 2204  wmo 2205 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1546  ax-5 1557  ax-17 1616  ax-9 1654  ax-8 1675  ax-6 1729  ax-7 1734  ax-11 1746  ax-12 1925 This theorem depends on definitions:  df-bi 177  df-or 359  df-an 360  df-tru 1319  df-ex 1542  df-nf 1545  df-sb 1649  df-eu 2208  df-mo 2209 This theorem is referenced by:  2exeu  2281
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