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Theorem elin3 3122
Description: Membership in a class defined as a ternary intersection. (Contributed by Stefan O'Rear, 29-Mar-2015.)
Hypothesis
Ref Expression
elin3.x  X  i^i  C  i^i  D
Assertion
Ref Expression
elin3  X  C  D

Proof of Theorem elin3
StepHypRef Expression
1 elin 3120 . . 3  i^i  C  C
21anbi1i 431 . 2  i^i  C  D  C  D
3 elin3.x . . 3  X  i^i  C  i^i  D
43elin2 3121 . 2  X  i^i  C  D
5 df-3an 886 . 2  C  D  C  D
62, 4, 53bitr4i 201 1  X  C  D
Colors of variables: wff set class
Syntax hints:   wa 97   wb 98   w3a 884   wceq 1242   wcel 1390    i^i cin 2910
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 99  ax-ia2 100  ax-ia3 101  ax-io 629  ax-5 1333  ax-7 1334  ax-gen 1335  ax-ie1 1379  ax-ie2 1380  ax-8 1392  ax-10 1393  ax-11 1394  ax-i12 1395  ax-bndl 1396  ax-4 1397  ax-17 1416  ax-i9 1420  ax-ial 1424  ax-i5r 1425  ax-ext 2019
This theorem depends on definitions:  df-bi 110  df-3an 886  df-tru 1245  df-nf 1347  df-sb 1643  df-clab 2024  df-cleq 2030  df-clel 2033  df-nfc 2164  df-v 2553  df-in 2918
This theorem is referenced by: (None)
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