NFE Home New Foundations Explorer < Previous   Next >
Nearby theorems
Mirrors  >  Home  >  NFE Home  >  Th. List  >  in12 Unicode version

Theorem in12 3466
Description: A rearrangement of intersection. (Contributed by NM, 21-Apr-2001.)
Assertion
Ref Expression
in12

Proof of Theorem in12
StepHypRef Expression
1 incom 3448 . . 3
21ineq1i 3453 . 2
3 inass 3465 . 2
4 inass 3465 . 2
52, 3, 43eqtr3i 2381 1
Colors of variables: wff setvar class
Syntax hints:   wceq 1642   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:  in32  3467  in31  3469  in4  3471  resdmres  5078
  Copyright terms: Public domain W3C validator