Intuitionistic Logic Explorer < Previous   Next > Nearby theorems Mirrors  >  Home  >  ILE Home  >  Th. List  >  ineqan12d Unicode version

Theorem ineqan12d 3170
 Description: Equality deduction for intersection of two classes. (Contributed by NM, 7-Feb-2007.)
Hypotheses
Ref Expression
ineq1d.1
ineqan12d.2
Assertion
Ref Expression
ineqan12d

Proof of Theorem ineqan12d
StepHypRef Expression
1 ineq1d.1 . 2
2 ineqan12d.2 . 2
3 ineq12 3163 . 2
41, 2, 3syl2an 283 1
 Colors of variables: wff set class Syntax hints:   wi 4   wa 102   wceq 1285   cin 2973 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 104  ax-ia2 105  ax-ia3 106  ax-io 663  ax-5 1377  ax-7 1378  ax-gen 1379  ax-ie1 1423  ax-ie2 1424  ax-8 1436  ax-10 1437  ax-11 1438  ax-i12 1439  ax-bndl 1440  ax-4 1441  ax-17 1460  ax-i9 1464  ax-ial 1468  ax-i5r 1469  ax-ext 2064 This theorem depends on definitions:  df-bi 115  df-tru 1288  df-nf 1391  df-sb 1687  df-clab 2069  df-cleq 2075  df-clel 2078  df-nfc 2209  df-v 2604  df-in 2980 This theorem is referenced by:  fvun1  5265  fndmin  5300  offval  5744  ofrfval  5745  offval3  5786
 Copyright terms: Public domain W3C validator