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Theorem 2rexreu 38616
 Description: Double restricted existential uniqueness implies double restricted uniqueness quantification, analogous to 2exeu 2380. (Contributed by Alexander van der Vekens, 25-Jun-2017.)
Assertion
Ref Expression
2rexreu
Distinct variable groups:   ,   ,   ,
Allowed substitution hints:   (,)   ()   ()

Proof of Theorem 2rexreu
StepHypRef Expression
1 reurmo 3012 . . . 4
2 reurex 3011 . . . . 5
32rmoimi 38607 . . . 4
41, 3syl 17 . . 3
5 2reurex 38612 . . 3
64, 5anim12ci 571 . 2
7 reu5 3010 . 2
86, 7sylibr 216 1
 Colors of variables: wff setvar class Syntax hints:   wi 4   wa 371  wrex 2740  wreu 2741  wrmo 2742 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1671  ax-4 1684  ax-5 1760  ax-6 1807  ax-7 1853  ax-10 1917  ax-11 1922  ax-12 1935  ax-13 2093  ax-ext 2433 This theorem depends on definitions:  df-bi 189  df-or 372  df-an 373  df-tru 1449  df-ex 1666  df-nf 1670  df-sb 1800  df-eu 2305  df-mo 2306  df-cleq 2446  df-clel 2449  df-nfc 2583  df-ral 2744  df-rex 2745  df-reu 2746  df-rmo 2747 This theorem is referenced by:  2reu1  38617  2reu2  38618  2reu3  38619
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