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Theorem reuan 38473
 Description: Introduction of a conjunct into restricted uniqueness quantifier, analogous to euan 2329. (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 458 . . . . . . 7
32a1i 11 . . . . . 6
41, 3rexlimi 2904 . . . . 5
54adantr 466 . . . 4
6 simpr 462 . . . . . 6
76reximi 2890 . . . . 5
87adantr 466 . . . 4
9 nfre1 2883 . . . . . 6
104adantr 466 . . . . . . . . 9
1110a1d 26 . . . . . . . 8
1211ancrd 556 . . . . . . 7
136, 12impbid2 207 . . . . . 6
149, 13rmobida 3013 . . . . 5
1514biimpa 486 . . . 4
165, 8, 15jca32 537 . . 3
17 reu5 3043 . . 3
18 reu5 3043 . . . 4
1918anbi2i 698 . . 3
2016, 17, 193imtr4i 269 . 2
21 ibar 506 . . . . 5
2221adantr 466 . . . 4
231, 22reubida 3008 . . 3
2423biimpa 486 . 2
2520, 24impbii 190 1
 Colors of variables: wff setvar class Syntax hints:   wi 4   wb 187   wa 370  wnf 1661   wcel 1872  wrex 2772  wreu 2773  wrmo 2774 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1663  ax-4 1676  ax-5 1752  ax-6 1798  ax-7 1843  ax-10 1891  ax-12 1909 This theorem depends on definitions:  df-bi 188  df-an 372  df-ex 1658  df-nf 1662  df-eu 2273  df-mo 2274  df-ral 2776  df-rex 2777  df-reu 2778  df-rmo 2779 This theorem is referenced by:  2reu7  38484  2reu8  38485
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