Theorem elab3gf 3251

Description: Membership in a class abstraction, with a weaker antecedent than elabgf 3244. (Contributed by NM, 6-Sep-2011.)

Hypotheses

Ref	Expression
elab3gf.1
elab3gf.2
elab3gf.3

Assertion

Ref	Expression
elab3gf

Proof of Theorem elab3gf

Step	Hyp	Ref	Expression
1		elab3gf.1	. . . . 5
2		elab3gf.2	. . . . 5
3		elab3gf.3	. . . . 5
4	1, 2, 3	elabgf 3244	. . . 4
5	4	ibi 241	. . 3
6		pm2.21 108	. . 3
7	5, 6	impbid2 204	. 2
8	1, 2, 3	elabgf 3244	. 2
9	7, 8	ja 161	1

Syntax hints:  -.wn 3  ->wi 4  <->wb 184  =wceq 1395  F/wnf 1616  e.wcel 1818  {cab 2442  F/_wnfc 2605

This theorem is referenced by:  elab3g  3252

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-v 3111