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Theorem 2reurex 28047
 Description: Double restricted quantification with existential uniqueness, analogous to 2euex 2360. (Contributed by Alexander van der Vekens, 24-Jun-2017.)
Assertion
Ref Expression
2reurex
Distinct variable groups:   ,   ,   ,
Allowed substitution hints:   (,)   ()   ()

Proof of Theorem 2reurex
StepHypRef Expression
1 reu5 2930 . 2
2 rexcom 2876 . . . 4
3 nfcv 2579 . . . . . 6
4 nfre1 2769 . . . . . 6
53, 4nfrmo 2890 . . . . 5
6 rspe 2774 . . . . . . . . . . 11
76ex 425 . . . . . . . . . 10
87ralrimivw 2797 . . . . . . . . 9
9 rmoim 3142 . . . . . . . . 9
108, 9syl 16 . . . . . . . 8
1110impcom 421 . . . . . . 7
12 rmo5 2933 . . . . . . 7
1311, 12sylib 190 . . . . . 6
1413ex 425 . . . . 5
155, 14reximdai 2821 . . . 4
162, 15syl5bi 210 . . 3
1716impcom 421 . 2
181, 17sylbi 189 1
 Colors of variables: wff set class Syntax hints:   wi 4   wa 360   wcel 1728  wral 2712  wrex 2713  wreu 2714  wrmo 2715 This theorem is referenced by:  2rexreu  28051 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1556  ax-5 1567  ax-17 1628  ax-9 1669  ax-8 1690  ax-6 1747  ax-7 1752  ax-11 1764  ax-12 1954  ax-ext 2424 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 1661  df-eu 2292  df-mo 2293  df-cleq 2436  df-clel 2439  df-nfc 2568  df-ral 2717  df-rex 2718  df-reu 2719  df-rmo 2720
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