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Theorem 2reuswap2 23975
 Description: A condition allowing swap of uniqueness and existential quantifiers. (Contributed by Thierry Arnoux, 7-Apr-2017.)
Assertion
Ref Expression
2reuswap2
Distinct variable groups:   ,,   ,
Allowed substitution hints:   (,)   ()

Proof of Theorem 2reuswap2
StepHypRef Expression
1 df-ral 2710 . . 3
2 moanimv 2339 . . . 4
32albii 1575 . . 3
41, 3bitr4i 244 . 2
5 2euswap 2357 . . 3
6 df-reu 2712 . . . 4
7 r19.42v 2862 . . . . . . 7
8 df-rex 2711 . . . . . . 7
97, 8bitr3i 243 . . . . . 6
10 an12 773 . . . . . . 7
1110exbii 1592 . . . . . 6
129, 11bitri 241 . . . . 5
1312eubii 2290 . . . 4
146, 13bitri 241 . . 3
15 df-reu 2712 . . . 4
16 r19.42v 2862 . . . . . 6
17 df-rex 2711 . . . . . 6
1816, 17bitr3i 243 . . . . 5
1918eubii 2290 . . . 4
2015, 19bitri 241 . . 3
215, 14, 203imtr4g 262 . 2
224, 21sylbi 188 1
 Colors of variables: wff set class Syntax hints:   wi 4   wa 359  wal 1549  wex 1550   wcel 1725  weu 2281  wmo 2282  wral 2705  wrex 2706  wreu 2707 This theorem is referenced by:  reuxfr3d  23976 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1555  ax-5 1566  ax-17 1626  ax-9 1666  ax-8 1687  ax-6 1744  ax-7 1749  ax-11 1761  ax-12 1950 This theorem depends on definitions:  df-bi 178  df-or 360  df-an 361  df-tru 1328  df-ex 1551  df-nf 1554  df-sb 1659  df-eu 2285  df-mo 2286  df-ral 2710  df-rex 2711  df-reu 2712
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