Theorem elrab3t 3256

Description: Membership in a restricted class abstraction, using implicit substitution. (Closed theorem version of elrab3 3258.) (Contributed by Thierry Arnoux, 31-Aug-2017.)

Assertion

Ref	Expression
elrab3t

Distinct variable groups:   ,   ,   ,

Proof of Theorem elrab3t

Step	Hyp	Ref	Expression
1		df-rab 2816	. . 3
2	1	eleq2i 2535	. 2
3		simpr 461	. . 3
4		nfa1 1897	. . . . 5
5		nfv 1707	. . . . 5
6	4, 5	nfan 1928	. . . 4
7		simpl 457	. . . . . 6
8	7	19.21bi 1869	. . . . 5
9		eleq1 2529	. . . . . . . . . 10
10	9	biimparc 487	. . . . . . . . 9
11	10	biantrurd 508	. . . . . . . 8
12	11	bibi1d 319	. . . . . . 7
13	12	pm5.74da 687	. . . . . 6
14	13	adantl 466	. . . . 5
15	8, 14	mpbid 210	. . . 4
16	6, 15	alrimi 1877	. . 3
17		elabgt 3243	. . 3
18	3, 16, 17	syl2anc 661	. 2
19	2, 18	syl5bb 257	1

Syntax hints:  ->wi 4  <->wb 184  /\wa 369  A.wal 1393  =wceq 1395  e.wcel 1818  {cab 2442  {crab 2811

This theorem is referenced by:  f1oresrab  6063

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-an 371  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-rab 2816  df-v 3111