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Theorem inteq 3929
 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 2807 . . 3
21abbidv 2467 . 2
3 dfint2 3928 . 2
4 dfint2 3928 . 2
52, 3, 43eqtr4g 2410 1
 Colors of variables: wff setvar class Syntax hints:   wi 4   wceq 1642   wcel 1710  cab 2339  wral 2614  cint 3926 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1546  ax-5 1557  ax-17 1616  ax-9 1654  ax-8 1675  ax-6 1729  ax-7 1734  ax-11 1746  ax-12 1925  ax-ext 2334 This theorem depends on definitions:  df-bi 177  df-or 359  df-an 360  df-tru 1319  df-ex 1542  df-nf 1545  df-sb 1649  df-clab 2340  df-cleq 2346  df-clel 2349  df-nfc 2478  df-ral 2619  df-int 3927 This theorem is referenced by:  inteqi  3930  inteqd  3931  unissint  3950  uniintsn  3963  rint0  3966  clos1eq1  5874  clos1eq2  5875
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