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Theorem 2reu5lem1 3305
Description: Lemma for 2reu5 3308. Note that does not mean "there is exactly one in and exactly one in such that holds;" see comment for 2eu5 2382. (Contributed by Alexander van der Vekens, 17-Jun-2017.)
Assertion
Ref Expression
2reu5lem1
Distinct variable groups:   ,   ,   ,

Proof of Theorem 2reu5lem1
StepHypRef Expression
1 df-reu 2814 . . 3
21reubii 3044 . 2
3 df-reu 2814 . . 3
4 euanv 2355 . . . . . 6
54bicomi 202 . . . . 5
6 3anass 977 . . . . . . 7
76bicomi 202 . . . . . 6
87eubii 2306 . . . . 5
95, 8bitri 249 . . . 4
109eubii 2306 . . 3
113, 10bitri 249 . 2
122, 11bitri 249 1
Colors of variables: wff setvar class
Syntax hints:  <->wb 184  /\wa 369  /\w3a 973  e.wcel 1818  E!weu 2282  E!wreu 2809
This theorem is referenced by:  2reu5lem3  3307
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1618  ax-4 1631  ax-5 1704  ax-6 1747  ax-7 1790  ax-10 1837  ax-12 1854
This theorem depends on definitions:  df-bi 185  df-an 371  df-3an 975  df-tru 1398  df-ex 1613  df-nf 1617  df-eu 2286  df-reu 2814
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