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Theorem relin2 4968
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 3683 . 2  |-  ( A  i^i  B )  C_  B
2 relss 4938 . 2  |-  ( ( A  i^i  B ) 
C_  B  ->  ( Rel  B  ->  Rel  ( A  i^i  B ) ) )
31, 2ax-mp 5 1  |-  ( Rel 
B  ->  Rel  ( A  i^i  B ) )
Colors of variables: wff setvar class
Syntax hints:    -> wi 4    i^i cin 3435    C_ wss 3436   Rel wrel 4855
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1665  ax-4 1678  ax-5 1748  ax-6 1794  ax-7 1839  ax-10 1887  ax-11 1892  ax-12 1905  ax-13 2053  ax-ext 2400
This theorem depends on definitions:  df-bi 188  df-an 372  df-tru 1440  df-ex 1660  df-nf 1664  df-sb 1787  df-clab 2408  df-cleq 2414  df-clel 2417  df-nfc 2572  df-v 3083  df-in 3443  df-ss 3450  df-rel 4857
This theorem is referenced by:  intasym  5231  asymref  5232  poirr2  5240  brdom3  8957  brdom5  8958  brdom4  8959
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