Theorem class2seteq 4620

Description: Equality theorem based on class2set 4619. (Contributed by NM, 13-Dec-2005.) (Proof shortened by Raph Levien, 30-Jun-2006.)

Assertion

Ref	Expression
class2seteq

Distinct variable group:   ,

Proof of Theorem class2seteq

Step	Hyp	Ref	Expression
1		elex 3118	. 2
2		ax-1 6	. . . . 5
3	2	ralrimiv 2869	. . . 4
4		rabid2 3035	. . . 4
5	3, 4	sylibr 212	. . 3
6	5	eqcomd 2465	. 2
7	1, 6	syl 16	1

Syntax hints:  ->wi 4  =wceq 1395  e.wcel 1818  A.wral 2807  {crab 2811  cvv 3109

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-ral 2812  df-rab 2816  df-v 3111