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Theorem 2reu5lem1 3141
 Description: Lemma for 2reu5 3144. Note that does not mean "there is exactly one in and exactly one in such that holds;" see comment for 2eu5 2367. (Contributed by Alexander van der Vekens, 17-Jun-2017.)
Assertion
Ref Expression
2reu5lem1
Distinct variable groups:   ,   ,   ,
Allowed substitution hints:   (,)   ()   ()

Proof of Theorem 2reu5lem1
StepHypRef Expression
1 df-reu 2714 . . 3
21reubii 2896 . 2
3 df-reu 2714 . . 3
4 euanv 2344 . . . . . 6
54bicomi 195 . . . . 5
6 3anass 941 . . . . . . 7
76bicomi 195 . . . . . 6
87eubii 2292 . . . . 5
95, 8bitri 242 . . . 4
109eubii 2292 . . 3
113, 10bitri 242 . 2
122, 11bitri 242 1
 Colors of variables: wff set class Syntax hints:   wb 178   wa 360   w3a 937   wcel 1726  weu 2283  wreu 2709 This theorem is referenced by:  2reu5lem3  3143 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1556  ax-5 1567  ax-17 1627  ax-9 1667  ax-8 1688  ax-6 1745  ax-7 1750  ax-11 1762  ax-12 1951 This theorem depends on definitions:  df-bi 179  df-or 361  df-an 362  df-3an 939  df-tru 1329  df-ex 1552  df-nf 1555  df-sb 1660  df-eu 2287  df-mo 2288  df-reu 2714
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