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

Step	Hyp	Ref	Expression
1		df-reu 2814	. . 3
2	1	reubii 3044	. 2
3		df-reu 2814	. . 3
4		euanv 2355	. . . . . 6
5	4	bicomi 202	. . . . 5
6		3anass 977	. . . . . . 7
7	6	bicomi 202	. . . . . 6
8	7	eubii 2306	. . . . 5
9	5, 8	bitri 249	. . . 4
10	9	eubii 2306	. . 3
11	3, 10	bitri 249	. 2
12	2, 11	bitri 249	1

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