Theorem elin3 3689

Description: Membership in a class defined as a ternary intersection. (Contributed by Stefan O'Rear, 29-Mar-2015.)

Hypothesis

Ref	Expression
elin3.x

Assertion

Ref	Expression
elin3

Proof of Theorem elin3

Step	Hyp	Ref	Expression
1		elin 3686	. . 3
2	1	anbi1i 695	. 2
3		elin3.x	. . 3
4	3	elin2 3688	. 2
5		df-3an 975	. 2
6	2, 4, 5	3bitr4i 277	1

Syntax hints:  <->wb 184  /\wa 369  /\w3a 973  =wceq 1395  e.wcel 1818  i^icin 3474

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-3an 975  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  df-in 3482