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

Theorem inteqd 3693
Description: Equality deduction for class intersection. (Contributed by NM, 2-Sep-2003.)
Hypothesis
Ref Expression
inteqd.1  |-  ( ph  ->  A  =  B )
Assertion
Ref Expression
inteqd  |-  ( ph  ->  |^| A  =  |^| B )

Proof of Theorem inteqd
StepHypRef Expression
1 inteqd.1 . 2  |-  ( ph  ->  A  =  B )
2 inteq 3691 . 2  |-  ( A  =  B  ->  |^| A  =  |^| B )
31, 2syl 14 1  |-  ( ph  ->  |^| A  =  |^| B )
Colors of variables: wff set class
Syntax hints:    -> wi 4    = wceq 1289   |^|cint 3688
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 665  ax-5 1381  ax-7 1382  ax-gen 1383  ax-ie1 1427  ax-ie2 1428  ax-8 1440  ax-10 1441  ax-11 1442  ax-i12 1443  ax-bndl 1444  ax-4 1445  ax-17 1464  ax-i9 1468  ax-ial 1472  ax-i5r 1473  ax-ext 2070
This theorem depends on definitions:  df-bi 115  df-tru 1292  df-nf 1395  df-sb 1693  df-clab 2075  df-cleq 2081  df-clel 2084  df-nfc 2217  df-ral 2364  df-int 3689
This theorem is referenced by:  intprg  3721  op1stbg  4301  onsucmin  4324  elreldm  4661  elxp5  4919  fniinfv  5362  1stval2  5926  2ndval2  5927  fundmen  6523  xpsnen  6537  fiintim  6639  cardcl  6809  isnumi  6810  cardval3ex  6813  carden2bex  6817
  Copyright terms: Public domain W3C validator