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Theorem 2eu3 2286
 Description: Double existential uniqueness. (Contributed by NM, 3-Dec-2001.)
Assertion
Ref Expression
2eu3

Proof of Theorem 2eu3
StepHypRef Expression
1 nfmo1 2215 . . . . 5
2119.31 1876 . . . 4
32albii 1566 . . 3
4 nfmo1 2215 . . . . 5
54nfal 1842 . . . 4
6519.32 1875 . . 3
73, 6bitri 240 . 2
8 2eu1 2284 . . . . . . 7
98biimpd 198 . . . . . 6
10 ancom 437 . . . . . 6
119, 10syl6ib 217 . . . . 5
1211adantld 453 . . . 4
13 2eu1 2284 . . . . . 6
1413biimpd 198 . . . . 5
1514adantrd 454 . . . 4
1612, 15jaoi 368 . . 3
17 2exeu 2281 . . . 4
18 2exeu 2281 . . . . 5
1918ancoms 439 . . . 4
2017, 19jca 518 . . 3
2116, 20impbid1 194 . 2
227, 21sylbi 187 1
 Colors of variables: wff setvar class Syntax hints:   wi 4   wb 176   wo 357   wa 358  wal 1540  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: (None)
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