Intuitionistic Logic Explorer < Previous   Next > Nearby theorems Mirrors  >  Home  >  ILE Home  >  Th. List  >  ineq12d Unicode version

Theorem ineq12d 3273
 Description: Equality deduction for intersection of two classes. (Contributed by NM, 24-Jun-2004.) (Proof shortened by Andrew Salmon, 26-Jun-2011.)
Hypotheses
Ref Expression
ineq1d.1
ineq12d.2
Assertion
Ref Expression
ineq12d

Proof of Theorem ineq12d
StepHypRef Expression
1 ineq1d.1 . 2
2 ineq12d.2 . 2
3 ineq12 3267 . 2
41, 2, 3syl2anc 408 1
 Colors of variables: wff set class Syntax hints:   wi 4   wceq 1331   cin 3065 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 698  ax-5 1423  ax-7 1424  ax-gen 1425  ax-ie1 1469  ax-ie2 1470  ax-8 1482  ax-10 1483  ax-11 1484  ax-i12 1485  ax-bndl 1486  ax-4 1487  ax-17 1506  ax-i9 1510  ax-ial 1514  ax-i5r 1515  ax-ext 2119 This theorem depends on definitions:  df-bi 116  df-tru 1334  df-nf 1437  df-sb 1736  df-clab 2124  df-cleq 2130  df-clel 2133  df-nfc 2268  df-v 2683  df-in 3072 This theorem is referenced by:  csbing  3278  funprg  5168  funtpg  5169  offval  5982  ofrfval  5983  undifdc  6805  djudom  6971  ressid2  12007  ressval2  12008
 Copyright terms: Public domain W3C validator