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Theorem inteq 3618
 Description: Equality law for intersection. (Contributed by NM, 13-Sep-1999.)
Assertion
Ref Expression
inteq

Proof of Theorem inteq
Dummy variables are mutually distinct and distinct from all other variables.
StepHypRef Expression
1 raleq 2505 . . 3
21abbidv 2155 . 2
3 dfint2 3617 . 2
4 dfint2 3617 . 2
52, 3, 43eqtr4g 2097 1
 Colors of variables: wff set class Syntax hints:   wi 4   wceq 1243  cab 2026  wral 2306  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:  inteqi  3619  inteqd  3620  uniintsnr  3651  rint0  3654  intexr  3904  onintexmid  4297  elreldm  4560  elxp5  4809  1stval2  5782  fundmen  6286  xpsnen  6295  bj-intexr  10028
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