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Theorem relin1 4978
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 3591 . 2  |-  ( A  i^i  B )  C_  A
2 relss 4948 . 2  |-  ( ( A  i^i  B ) 
C_  A  ->  ( Rel  A  ->  Rel  ( A  i^i  B ) ) )
31, 2ax-mp 5 1  |-  ( Rel 
A  ->  Rel  ( A  i^i  B ) )
Colors of variables: wff setvar class
Syntax hints:    -> wi 4    i^i cin 3348    C_ wss 3349   Rel wrel 4866
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1591  ax-4 1602  ax-5 1670  ax-6 1708  ax-7 1728  ax-10 1775  ax-11 1780  ax-12 1792  ax-13 1943  ax-ext 2423
This theorem depends on definitions:  df-bi 185  df-an 371  df-tru 1372  df-ex 1587  df-nf 1590  df-sb 1701  df-clab 2430  df-cleq 2436  df-clel 2439  df-nfc 2577  df-v 2995  df-in 3356  df-ss 3363  df-rel 4868
This theorem is referenced by:  inopab  4991  idsset  27943  dihmeetlem1N  35031  dihglblem5apreN  35032  dihmeetlem4preN  35047  dihmeetlem13N  35060
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