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Theorem 2eu1 2376
 Description: Double existential uniqueness. This theorem shows a condition under which a "naive" definition matches the correct one. (Contributed by NM, 3-Dec-2001.) (Proof shortened by Wolf Lammen, 11-Nov-2019.)
Assertion
Ref Expression
2eu1

Proof of Theorem 2eu1
StepHypRef Expression
1 2eu2ex 2368 . . . . 5
2 df-mo 2287 . . . . . . 7
32albii 1640 . . . . . 6
4 euim 2344 . . . . . . 7
54ex 434 . . . . . 6
63, 5syl5bi 217 . . . . 5
71, 6syl 16 . . . 4
87pm2.43b 50 . . 3
9 2euswap 2370 . . . 4
108, 9syld 44 . . 3
 Colors of variables: wff setvar class Syntax hints:  ->wi 4  <->wb 184  /\wa 369  A.wal 1393  E.wex 1612  E!weu 2282  E*wmo 2283 This theorem is referenced by:  2eu2  2378  2eu3  2379  2eu5  2382 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-or 370  df-an 371  df-tru 1398  df-ex 1613  df-nf 1617  df-eu 2286  df-mo 2287