Theorem ceqsalt 3132

Description: Closed theorem version of ceqsalg 3134. (Contributed by NM, 28-Feb-2013.) (Revised by Mario Carneiro, 10-Oct-2016.)

Assertion

Ref	Expression
ceqsalt

Distinct variable group:   ,

Proof of Theorem ceqsalt

Step	Hyp	Ref	Expression
1		elisset 3120	. . . 4
2	1	3ad2ant3 1019	. . 3
3		bi1 186	. . . . . . 7
4	3	imim3i 59	. . . . . 6
5	4	al2imi 1636	. . . . 5
6	5	3ad2ant2 1018	. . . 4
7		19.23t 1909	. . . . 5
8	7	3ad2ant1 1017	. . . 4
9	6, 8	sylibd 214	. . 3
10	2, 9	mpid 41	. 2
11		bi2 198	. . . . . . 7
12	11	imim2i 14	. . . . . 6
13	12	com23 78	. . . . 5
14	13	alimi 1633	. . . 4
15	14	3ad2ant2 1018	. . 3
16		19.21t 1904	. . . 4
17	16	3ad2ant1 1017	. . 3
18	15, 17	mpbid 210	. 2
19	10, 18	impbid 191	1

Syntax hints:  ->wi 4  <->wb 184  /\w3a 973  A.wal 1393  =wceq 1395  E.wex 1612  F/wnf 1616  e.wcel 1818

This theorem is referenced by:  ceqsralt  3133  ceqsalg  3134

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  ax-ext 2435

This theorem depends on definitions:  df-bi 185  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-v 3111