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Theorem relin2 4995
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 3564 . 2  |-  ( A  i^i  B )  C_  B
2 relss 4965 . 2  |-  ( ( A  i^i  B ) 
C_  B  ->  ( Rel  B  ->  Rel  ( A  i^i  B ) ) )
31, 2ax-mp 8 1  |-  ( Rel 
B  ->  Rel  ( A  i^i  B ) )
Colors of variables: wff set class
Syntax hints:    -> wi 4    i^i cin 3321    C_ wss 3322   Rel wrel 4885
This theorem is referenced by:  intasym  5251  asymref  5252  poirr2  5260  brdom3  8408  brdom5  8409  brdom4  8410
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1556  ax-5 1567  ax-17 1627  ax-9 1667  ax-8 1688  ax-6 1745  ax-7 1750  ax-11 1762  ax-12 1951  ax-ext 2419
This theorem depends on definitions:  df-bi 179  df-or 361  df-an 362  df-tru 1329  df-ex 1552  df-nf 1555  df-sb 1660  df-clab 2425  df-cleq 2431  df-clel 2434  df-nfc 2563  df-v 2960  df-in 3329  df-ss 3336  df-rel 4887
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