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Theorem relin2 4841
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 3424 . 2  |-  ( A  i^i  B )  C_  B
2 relss 4812 . 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 3185    C_ wss 3186   Rel wrel 4731
This theorem is referenced by:  intasym  5095  asymref  5096  poirr2  5104  brdom3  8198  brdom5  8199  brdom4  8200
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1537  ax-5 1548  ax-17 1607  ax-9 1645  ax-8 1666  ax-6 1720  ax-7 1725  ax-11 1732  ax-12 1897  ax-ext 2297
This theorem depends on definitions:  df-bi 177  df-or 359  df-an 360  df-tru 1310  df-ex 1533  df-nf 1536  df-sb 1640  df-clab 2303  df-cleq 2309  df-clel 2312  df-nfc 2441  df-v 2824  df-in 3193  df-ss 3200  df-rel 4733
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