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

Theorem inteqi 3619
Description: Equality inference for class intersection. (Contributed by NM, 2-Sep-2003.)
Hypothesis
Ref Expression
inteqi.1  |-  A  =  B
Assertion
Ref Expression
inteqi  |-  |^| A  =  |^| B

Proof of Theorem inteqi
StepHypRef Expression
1 inteqi.1 . 2  |-  A  =  B
2 inteq 3618 . 2  |-  ( A  =  B  ->  |^| A  =  |^| B )
31, 2ax-mp 7 1  |-  |^| A  =  |^| B
Colors of variables: wff set class
Syntax hints:    = wceq 1243   |^|cint 3615
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 99  ax-ia2 100  ax-ia3 101  ax-io 630  ax-5 1336  ax-7 1337  ax-gen 1338  ax-ie1 1382  ax-ie2 1383  ax-8 1395  ax-10 1396  ax-11 1397  ax-i12 1398  ax-bndl 1399  ax-4 1400  ax-17 1419  ax-i9 1423  ax-ial 1427  ax-i5r 1428  ax-ext 2022
This theorem depends on definitions:  df-bi 110  df-tru 1246  df-nf 1350  df-sb 1646  df-clab 2027  df-cleq 2033  df-clel 2036  df-nfc 2167  df-ral 2311  df-int 3616
This theorem is referenced by:  elintrab  3627  ssintrab  3638  intmin2  3641  intsng  3649  intexrabim  3907  op1stb  4209  bm2.5ii  4222  dfiin3g  4590  op2ndb  4804  bj-dfom  10057  bj-omind  10058
  Copyright terms: Public domain W3C validator