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Theorem dfin5 2919
 Description: Alternate definition for the intersection of two classes. (Contributed by NM, 6-Jul-2005.)
Assertion
Ref Expression
dfin5 (AB) = {x Ax B}
Distinct variable groups:   x,A   x,B

Proof of Theorem dfin5
StepHypRef Expression
1 df-in 2918 . 2 (AB) = {x ∣ (x A x B)}
2 df-rab 2309 . 2 {x Ax B} = {x ∣ (x A x B)}
31, 2eqtr4i 2060 1 (AB) = {x Ax B}
 Colors of variables: wff set class Syntax hints:   ∧ wa 97   = wceq 1242   ∈ wcel 1390  {cab 2023  {crab 2304   ∩ cin 2910 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-gen 1335  ax-4 1397  ax-17 1416  ax-ext 2019 This theorem depends on definitions:  df-bi 110  df-cleq 2030  df-rab 2309  df-in 2918 This theorem is referenced by:  nfin  3137  rabbi2dva  3139  bj-inex  9292
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