Intuitionistic Logic Explorer < Previous   Next > Nearby theorems Mirrors  >  Home  >  ILE Home  >  Th. List  >  ineq12 Unicode version

Theorem ineq12 3278
 Description: Equality theorem for intersection of two classes. (Contributed by NM, 8-May-1994.)
Assertion
Ref Expression
ineq12

Proof of Theorem ineq12
StepHypRef Expression
1 ineq1 3276 . 2
2 ineq2 3277 . 2
31, 2sylan9eq 2193 1
 Colors of variables: wff set class Syntax hints:   wi 4   wa 103   wceq 1332   cin 3076 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 105  ax-ia2 106  ax-ia3 107  ax-io 699  ax-5 1424  ax-7 1425  ax-gen 1426  ax-ie1 1470  ax-ie2 1471  ax-8 1483  ax-10 1484  ax-11 1485  ax-i12 1486  ax-bndl 1487  ax-4 1488  ax-17 1507  ax-i9 1511  ax-ial 1515  ax-i5r 1516  ax-ext 2122 This theorem depends on definitions:  df-bi 116  df-tru 1335  df-nf 1438  df-sb 1737  df-clab 2127  df-cleq 2133  df-clel 2136  df-nfc 2271  df-v 2692  df-in 3083 This theorem is referenced by:  ineq12i  3281  ineq12d  3284  ineqan12d  3285  fnun  5239  endisj  6728  sbthlemi8  6865  pm54.43  7069  epttop  12321  restbasg  12399  txbas  12489  bj-inex  13309
 Copyright terms: Public domain W3C validator