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Theorem 2exeu 2360
 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 2323 . . . 4
2 euex 2306 . . . . 5
32moimi 2330 . . . 4
41, 3syl 16 . . 3
5 2euex 2355 . . 3
64, 5anim12ci 552 . 2
7 eu5 2321 . 2
86, 7sylibr 205 1
 Colors of variables: wff set class Syntax hints:   wi 4   wa 360  wex 1551  weu 2283  wmo 2284 This theorem is referenced by:  2eu1  2363  2eu2  2364  2eu3  2365 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1556  ax-5 1567  ax-17 1627  ax-9 1667  ax-8 1688  ax-6 1745  ax-7 1750  ax-11 1762  ax-12 1951 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 1660  df-eu 2287  df-mo 2288
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