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Theorem 2reu5lem1 3041
 Description: Lemma for 2reu5 3044. Note that does not mean "there is exactly one in and exactly one in such that holds;" see comment for 2eu5 2288. (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 2621 . . 3
21reubii 2797 . 2
3 df-reu 2621 . . 3
4 euanv 2265 . . . . . 6
54bicomi 193 . . . . 5
6 3anass 938 . . . . . . 7
76bicomi 193 . . . . . 6
87eubii 2213 . . . . 5
95, 8bitri 240 . . . 4
109eubii 2213 . . 3
113, 10bitri 240 . 2
122, 11bitri 240 1
 Colors of variables: wff setvar class Syntax hints:   wb 176   wa 358   w3a 934   wcel 1710  weu 2204  wreu 2616 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1546  ax-5 1557  ax-17 1616  ax-9 1654  ax-8 1675  ax-6 1729  ax-7 1734  ax-11 1746  ax-12 1925 This theorem depends on definitions:  df-bi 177  df-or 359  df-an 360  df-3an 936  df-tru 1319  df-ex 1542  df-nf 1545  df-sb 1649  df-eu 2208  df-mo 2209  df-reu 2621 This theorem is referenced by:  2reu5lem3  3043
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