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Theorem 2reuswap 3230
 Description: A condition allowing swap of uniqueness and existential quantifiers. (Contributed by Thierry Arnoux, 7-Apr-2017.) (Revised by NM, 16-Jun-2017.)
Assertion
Ref Expression
2reuswap
Distinct variable groups:   ,,   ,
Allowed substitution hints:   (,)   ()

Proof of Theorem 2reuswap
StepHypRef Expression
1 df-rmo 2764 . . 3
21ralbii 2823 . 2
3 df-ral 2761 . . . 4
4 moanimv 2380 . . . . 5
54albii 1699 . . . 4
63, 5bitr4i 260 . . 3
7 2euswap 2397 . . . 4
8 df-reu 2763 . . . . 5
9 r19.42v 2931 . . . . . . . 8
10 df-rex 2762 . . . . . . . 8
119, 10bitr3i 259 . . . . . . 7
12 an12 814 . . . . . . . 8
1312exbii 1726 . . . . . . 7
1411, 13bitri 257 . . . . . 6
1514eubii 2341 . . . . 5
168, 15bitri 257 . . . 4
17 df-reu 2763 . . . . 5
18 r19.42v 2931 . . . . . . 7
19 df-rex 2762 . . . . . . 7
2018, 19bitr3i 259 . . . . . 6
2120eubii 2341 . . . . 5
2217, 21bitri 257 . . . 4
237, 16, 223imtr4g 278 . . 3
246, 23sylbi 200 . 2
252, 24sylbi 200 1
 Colors of variables: wff setvar class Syntax hints:   wi 4   wa 376  wal 1450  wex 1671   wcel 1904  weu 2319  wmo 2320  wral 2756  wrex 2757  wreu 2758  wrmo 2759 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1677  ax-4 1690  ax-5 1766  ax-6 1813  ax-7 1859  ax-10 1932  ax-11 1937  ax-12 1950  ax-13 2104 This theorem depends on definitions:  df-bi 190  df-or 377  df-an 378  df-tru 1455  df-ex 1672  df-nf 1676  df-eu 2323  df-mo 2324  df-ral 2761  df-rex 2762  df-reu 2763  df-rmo 2764 This theorem is referenced by:  reuxfr2d  4623  reuxfr3d  28204
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