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Theorem relin1 4625
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 3264 . 2  |-  ( A  i^i  B )  C_  A
2 relss 4594 . 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 set class
Syntax hints:    -> wi 4    i^i cin 3038    C_ wss 3039   Rel wrel 4512
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 105  ax-ia2 106  ax-ia3 107  ax-io 681  ax-5 1406  ax-7 1407  ax-gen 1408  ax-ie1 1452  ax-ie2 1453  ax-8 1465  ax-10 1466  ax-11 1467  ax-i12 1468  ax-bndl 1469  ax-4 1470  ax-17 1489  ax-i9 1493  ax-ial 1497  ax-i5r 1498  ax-ext 2097
This theorem depends on definitions:  df-bi 116  df-tru 1317  df-nf 1420  df-sb 1719  df-clab 2102  df-cleq 2108  df-clel 2111  df-nfc 2245  df-v 2660  df-in 3045  df-ss 3052  df-rel 4514
This theorem is referenced by:  inopab  4639
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