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Theorem relin1 4819
Description: The intersection with a relation is a relation. (Contributed by NM, 16-Aug-1994.)
Assertion
Ref Expression
relin1  |-  ( Rel 
A  ->  Rel  ( A  i^i  B ) )

Proof of Theorem relin1
StepHypRef Expression
1 inss1 3402 . 2  |-  ( A  i^i  B )  C_  A
2 relss 4791 . 2  |-  ( ( A  i^i  B ) 
C_  A  ->  ( Rel  A  ->  Rel  ( A  i^i  B ) ) )
31, 2ax-mp 8 1  |-  ( Rel 
A  ->  Rel  ( A  i^i  B ) )
Colors of variables: wff set class
Syntax hints:    -> wi 4    i^i cin 3164    C_ wss 3165   Rel wrel 4710
This theorem is referenced by:  inopab  4832  idsset  24501  int2pre  25340  dihmeetlem1N  32102  dihglblem5apreN  32103  dihmeetlem4preN  32118  dihmeetlem13N  32131
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1536  ax-5 1547  ax-17 1606  ax-9 1644  ax-8 1661  ax-6 1715  ax-7 1720  ax-11 1727  ax-12 1878  ax-ext 2277
This theorem depends on definitions:  df-bi 177  df-or 359  df-an 360  df-tru 1310  df-ex 1532  df-nf 1535  df-sb 1639  df-clab 2283  df-cleq 2289  df-clel 2292  df-nfc 2421  df-v 2803  df-in 3172  df-ss 3179  df-rel 4712
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