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Theorem inteqd 3864
Description: Equality deduction for class intersection. (Contributed by NM, 2-Sep-2003.)
Hypothesis
Ref Expression
inteqd.1 (𝜑𝐴 = 𝐵)
Assertion
Ref Expression
inteqd (𝜑 𝐴 = 𝐵)

Proof of Theorem inteqd
StepHypRef Expression
1 inteqd.1 . 2 (𝜑𝐴 = 𝐵)
2 inteq 3862 . 2 (𝐴 = 𝐵 𝐴 = 𝐵)
31, 2syl 14 1 (𝜑 𝐴 = 𝐵)
Colors of variables: wff set class
Syntax hints:  wi 4   = wceq 1364   cint 3859
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 106  ax-ia2 107  ax-ia3 108  ax-io 710  ax-5 1458  ax-7 1459  ax-gen 1460  ax-ie1 1504  ax-ie2 1505  ax-8 1515  ax-10 1516  ax-11 1517  ax-i12 1518  ax-bndl 1520  ax-4 1521  ax-17 1537  ax-i9 1541  ax-ial 1545  ax-i5r 1546  ax-ext 2171
This theorem depends on definitions:  df-bi 117  df-tru 1367  df-nf 1472  df-sb 1774  df-clab 2176  df-cleq 2182  df-clel 2185  df-nfc 2321  df-ral 2473  df-int 3860
This theorem is referenced by:  intprg  3892  op1stbg  4497  onsucmin  4524  elreldm  4871  elxp5  5135  fniinfv  5595  1stval2  6181  2ndval2  6182  fundmen  6833  xpsnen  6848  fiintim  6958  elfi2  7002  fi0  7005  cardcl  7211  isnumi  7212  cardval3ex  7215  carden2bex  7219  lspfval  13721  lspval  13723  lsppropd  13765  clsfval  14078  clsval  14088
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