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Theorem reuan 27925
 Description: Introduction of a conjunct into restricted uniqueness quantifier, analogous to euan 2337. (Contributed by Alexander van der Vekens, 2-Jul-2017.)
Hypothesis
Ref Expression
rmoanim.1
Assertion
Ref Expression
reuan
Distinct variable group:   ,
Allowed substitution hints:   ()   ()

Proof of Theorem reuan
StepHypRef Expression
1 rmoanim.1 . . . . . 6
2 simpl 444 . . . . . . 7
32a1i 11 . . . . . 6
41, 3rexlimi 2815 . . . . 5
54adantr 452 . . . 4
6 simpr 448 . . . . . 6
76reximi 2805 . . . . 5
87adantr 452 . . . 4
9 nfre1 2754 . . . . . 6
104adantr 452 . . . . . . . . 9
1110a1d 23 . . . . . . . 8
1211ancrd 538 . . . . . . 7
136, 12impbid2 196 . . . . . 6
149, 13rmobida 2887 . . . . 5
1514biimpa 471 . . . 4
165, 8, 15jca32 522 . . 3
17 reu5 2913 . . 3
18 reu5 2913 . . . 4
1918anbi2i 676 . . 3
2016, 17, 193imtr4i 258 . 2
21 ibar 491 . . . . 5
2221adantr 452 . . . 4
231, 22reubida 2882 . . 3
2423biimpa 471 . 2
2520, 24impbii 181 1
 Colors of variables: wff set class Syntax hints:   wi 4   wb 177   wa 359  wnf 1553   wcel 1725  wrex 2698  wreu 2699  wrmo 2700 This theorem is referenced by:  2reu7  27936  2reu8  27937 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 2284  df-mo 2285  df-ral 2702  df-rex 2703  df-reu 2704  df-rmo 2705
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