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Theorem 2reu5lem1 3309
 Description: Lemma for 2reu5 3312. Note that does not mean "there is exactly one in and exactly one in such that holds;" see comment for 2eu5 2392. (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 2821 . . 3
21reubii 3048 . 2
3 df-reu 2821 . . 3
4 euanv 2360 . . . . . 6
54bicomi 202 . . . . 5
6 3anass 977 . . . . . . 7
76bicomi 202 . . . . . 6
87eubii 2300 . . . . 5
95, 8bitri 249 . . . 4
109eubii 2300 . . 3
113, 10bitri 249 . 2
122, 11bitri 249 1
 Colors of variables: wff setvar class Syntax hints:   wb 184   wa 369   w3a 973   wcel 1767  weu 2275  wreu 2816 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1601  ax-4 1612  ax-5 1680  ax-6 1719  ax-7 1739  ax-10 1786  ax-12 1803 This theorem depends on definitions:  df-bi 185  df-an 371  df-3an 975  df-tru 1382  df-ex 1597  df-nf 1600  df-eu 2279  df-reu 2821 This theorem is referenced by:  2reu5lem3  3311
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