Theorem ssunpr 4192

Description: Possible values for a set sandwiched between another set and it plus a singleton. (Contributed by Mario Carneiro, 2-Jul-2016.)

Assertion

Ref	Expression
ssunpr

Proof of Theorem ssunpr

Step	Hyp	Ref	Expression
1		df-pr 4032	. . . . . 6
2	1	uneq2i 3654	. . . . 5
3		unass 3660	. . . . 5
4	2, 3	eqtr4i 2489	. . . 4
5	4	sseq2i 3528	. . 3
6	5	anbi2i 694	. 2
7		ssunsn2 4189	. 2
8		ssunsn 4190	. . 3
9		un23 3662	. . . . . 6
10	9	sseq2i 3528	. . . . 5
11	10	anbi2i 694	. . . 4
12		ssunsn 4190	. . . 4
13	4, 9	eqtr2i 2487	. . . . . 6
14	13	eqeq2i 2475	. . . . 5
15	14	orbi2i 519	. . . 4
16	11, 12, 15	3bitri 271	. . 3
17	8, 16	orbi12i 521	. 2
18	6, 7, 17	3bitri 271	1

Syntax hints:  <->wb 184  \/wo 368  /\wa 369  =wceq 1395  u.cun 3473  C_wss 3475  {csn 4029  {cpr 4031

This theorem is referenced by:  sspr  4193  sstp  4194

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-11 1842  ax-12 1854  ax-13 1999  ax-ext 2435

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-ral 2812  df-v 3111  df-dif 3478  df-un 3480  df-in 3482  df-ss 3489  df-nul 3785  df-sn 4030  df-pr 4032