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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
StepHypRef Expression
1 elin 3686 . . 3
21anbi1i 695 . 2
3 elin3.x . . 3
43elin2 3688 . 2
5 df-3an 975 . 2
62, 4, 53bitr4i 277 1
 Colors of variables: wff setvar class 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
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