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Theorem 2exeu 2371
Description: Double existential uniqueness implies double uniqueness quantification. (Contributed by NM, 3-Dec-2001.) (Proof shortened by Mario Carneiro, 22-Dec-2016.)
Assertion
Ref Expression
2exeu

Proof of Theorem 2exeu
StepHypRef Expression
1 eumo 2313 . . . 4
2 euex 2308 . . . . 5
32moimi 2340 . . . 4
41, 3syl 16 . . 3
5 2euex 2366 . . 3
64, 5anim12ci 567 . 2
7 eu5 2310 . 2
86, 7sylibr 212 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:  2eu1  2376  2eu1OLD  2377  2eu2  2378  2eu3  2379
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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