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Theorem elin2 3446
Description: Membership in a class defined as an intersection. (Contributed by Stefan O'Rear, 29-Mar-2015.)
Hypothesis
Ref Expression
elin2.x X = (BC)
Assertion
Ref Expression
elin2 (A X ↔ (A B A C))

Proof of Theorem elin2
StepHypRef Expression
1 elin2.x . . 3 X = (BC)
21eleq2i 2417 . 2 (A XA (BC))
3 elin 3219 . 2 (A (BC) ↔ (A B A C))
42, 3bitri 240 1 (A X ↔ (A B A C))
Colors of variables: wff setvar class
Syntax hints:  wb 176   wa 358   = wceq 1642   wcel 1710  cin 3208
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1546  ax-5 1557  ax-17 1616  ax-9 1654  ax-8 1675  ax-6 1729  ax-7 1734  ax-11 1746  ax-12 1925  ax-ext 2334
This theorem depends on definitions:  df-bi 177  df-or 359  df-an 360  df-nan 1288  df-tru 1319  df-ex 1542  df-nf 1545  df-sb 1649  df-clab 2340  df-cleq 2346  df-clel 2349  df-nfc 2478  df-v 2861  df-nin 3211  df-compl 3212  df-in 3213
This theorem is referenced by:  elin3  3447  fnres  5199
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