Theorem ceqsralt 3133

Description: Restricted quantifier version of ceqsalt 3132. (Contributed by NM, 28-Feb-2013.) (Revised by Mario Carneiro, 10-Oct-2016.)

Assertion

Ref	Expression
ceqsralt

Distinct variable groups:   ,   ,

Proof of Theorem ceqsralt

Step	Hyp	Ref	Expression
1		df-ral 2812	. . . 4
2		eleq1 2529	. . . . . . . . 9
3	2	pm5.32ri 638	. . . . . . . 8
4	3	imbi1i 325	. . . . . . 7
5		impexp 446	. . . . . . 7
6		impexp 446	. . . . . . 7
7	4, 5, 6	3bitr3i 275	. . . . . 6
8	7	albii 1640	. . . . 5
9	8	a1i 11	. . . 4
10	1, 9	syl5bb 257	. . 3
11		19.21v 1729	. . 3
12	10, 11	syl6bb 261	. 2
13		biimt 335	. . 3
14	13	3ad2ant3 1019	. 2
15		ceqsalt 3132	. 2
16	12, 14, 15	3bitr2d 281	1

Syntax hints:  ->wi 4  <->wb 184  /\wa 369  /\w3a 973  A.wal 1393  =wceq 1395  F/wnf 1616  e.wcel 1818  A.wral 2807

This theorem is referenced by:  ceqsralv  3138  cdleme32fva  36163

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-ral 2812  df-v 3111