Theorem marypha2lem2 7916

Description: Lemma for marypha2 7919. Properties of the used relation. (Contributed by Stefan O'Rear, 20-Feb-2015.)

Hypothesis

Ref	Expression
marypha2lem.t

Assertion

Ref	Expression
marypha2lem2

Distinct variable groups:   ,,   ,,

Proof of Theorem marypha2lem2

Dummy variable is distinct from all other variables.

Step	Hyp	Ref	Expression
1		marypha2lem.t	. 2
2		sneq 4039	. . . 4
3		fveq2 5871	. . . 4
4	2, 3	xpeq12d 5029	. . 3
5	4	cbviunv 4369	. 2
6		df-xp 5010	. . . . 5
7	6	a1i 11	. . . 4
8	7	iuneq2i 4349	. . 3
9		iunopab 4788	. . 3
10		elsn 4043	. . . . . . . 8
11		equcom 1794	. . . . . . . 8
12	10, 11	bitri 249	. . . . . . 7
13	12	anbi1i 695	. . . . . 6
14	13	rexbii 2959	. . . . 5
15		fveq2 5871	. . . . . . 7
16	15	eleq2d 2527	. . . . . 6
17	16	ceqsrexbv 3234	. . . . 5
18	14, 17	bitri 249	. . . 4
19	18	opabbii 4516	. . 3
20	8, 9, 19	3eqtri 2490	. 2
21	1, 5, 20	3eqtri 2490	1

Syntax hints:  /\wa 369  =wceq 1395  e.wcel 1818  E.wrex 2808  {csn 4029  U_ciun 4330  {copab 4509  X.cxp 5002  `cfv 5593

This theorem is referenced by:  marypha2lem3  7917  marypha2lem4  7918  eulerpartlemgu  28316

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-9 1822  ax-10 1837  ax-11 1842  ax-12 1854  ax-13 1999  ax-ext 2435  ax-sep 4573  ax-nul 4581  ax-pr 4691

This theorem depends on definitions:  df-bi 185  df-or 370  df-an 371  df-3an 975  df-tru 1398  df-ex 1613  df-nf 1617  df-sb 1740  df-clab 2443  df-cleq 2449  df-clel 2452  df-nfc 2607  df-ne 2654  df-ral 2812  df-rex 2813  df-rab 2816  df-v 3111  df-dif 3478  df-un 3480  df-in 3482  df-ss 3489  df-nul 3785  df-if 3942  df-sn 4030  df-pr 4032  df-op 4036  df-uni 4250  df-iun 4332  df-br 4453  df-opab 4511  df-xp 5010  df-iota 5556  df-fv 5601