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Theorem inteqi 4056
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 4055 . 2  |-  ( A  =  B  ->  |^| A  =  |^| B )
31, 2ax-mp 8 1  |-  |^| A  =  |^| B
Colors of variables: wff set class
Syntax hints:    = wceq 1653   |^|cint 4052
This theorem is referenced by:  elintrab  4064  ssintrab  4075  intmin2  4079  intsng  4087  intexrab  4361  intabs  4363  ordintdif  4632  op1stb  4760  bm2.5ii  4788  dfiin3g  5125  op2ndb  5355  knatar  6082  oawordeulem  6799  oeeulem  6846  iinfi  7424  tcsni  7684  rankval2  7746  rankval3b  7754  cf0  8133  cfval2  8142  cofsmo  8151  isf34lem4  8259  isf34lem7  8261  sstskm  8719  dfnn3  10016  cycsubg  14970  efgval2  15358  00lsp  16059  alexsublem  18077  imaiinfv  26742  elrfi  26750
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1556  ax-5 1567  ax-17 1627  ax-9 1667  ax-8 1688  ax-6 1745  ax-7 1750  ax-11 1762  ax-12 1951  ax-ext 2419
This theorem depends on definitions:  df-bi 179  df-or 361  df-an 362  df-tru 1329  df-ex 1552  df-nf 1555  df-sb 1660  df-clab 2425  df-cleq 2431  df-clel 2434  df-nfc 2563  df-ral 2712  df-int 4053
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