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Theorem dfint2 3608
 Description: Alternate definition of class intersection. (Contributed by NM, 28-Jun-1998.)
Assertion
Ref Expression
dfint2 A = {xy A x y}
Distinct variable group:   x,y,A

Proof of Theorem dfint2
StepHypRef Expression
1 df-int 3607 . 2 A = {xy(y Ax y)}
2 df-ral 2305 . . 3 (y A x yy(y Ax y))
32abbii 2150 . 2 {xy A x y} = {xy(y Ax y)}
41, 3eqtr4i 2060 1 A = {xy A x y}
 Colors of variables: wff set class Syntax hints:   → wi 4  ∀wal 1240   = wceq 1242   ∈ wcel 1390  {cab 2023  ∀wral 2300  ∩ cint 3606 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-5 1333  ax-7 1334  ax-gen 1335  ax-ie1 1379  ax-ie2 1380  ax-8 1392  ax-11 1394  ax-4 1397  ax-17 1416  ax-i9 1420  ax-ial 1424  ax-i5r 1425  ax-ext 2019 This theorem depends on definitions:  df-bi 110  df-tru 1245  df-nf 1347  df-sb 1643  df-clab 2024  df-cleq 2030  df-ral 2305  df-int 3607 This theorem is referenced by:  inteq  3609  nfint  3616  intiin  3702
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