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Theorem relin2 4484
Description: The intersection with a relation is a relation. (Contributed by NM, 17-Jan-2006.)
Assertion
Ref Expression
relin2  |-  ( Rel 
B  ->  Rel  ( A  i^i  B ) )

Proof of Theorem relin2
StepHypRef Expression
1 inss2 3194 . 2  |-  ( A  i^i  B )  C_  B
2 relss 4453 . 2  |-  ( ( A  i^i  B ) 
C_  B  ->  ( Rel  B  ->  Rel  ( A  i^i  B ) ) )
31, 2ax-mp 7 1  |-  ( Rel 
B  ->  Rel  ( A  i^i  B ) )
Colors of variables: wff set class
Syntax hints:    -> wi 4    i^i cin 2973    C_ wss 2974   Rel wrel 4376
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 104  ax-ia2 105  ax-ia3 106  ax-io 663  ax-5 1377  ax-7 1378  ax-gen 1379  ax-ie1 1423  ax-ie2 1424  ax-8 1436  ax-10 1437  ax-11 1438  ax-i12 1439  ax-bndl 1440  ax-4 1441  ax-17 1460  ax-i9 1464  ax-ial 1468  ax-i5r 1469  ax-ext 2064
This theorem depends on definitions:  df-bi 115  df-tru 1288  df-nf 1391  df-sb 1687  df-clab 2069  df-cleq 2075  df-clel 2078  df-nfc 2209  df-v 2604  df-in 2980  df-ss 2987  df-rel 4378
This theorem is referenced by:  intasym  4739  asymref  4740  poirr2  4747
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