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Theorem reldif 4971
Description: A difference cutting down a relation is a relation. (Contributed by NM, 31-Mar-1998.)
Assertion
Ref Expression
reldif  |-  ( Rel 
A  ->  Rel  ( A 
\  B ) )

Proof of Theorem reldif
StepHypRef Expression
1 difss 3571 . 2  |-  ( A 
\  B )  C_  A
2 relss 4940 . 2  |-  ( ( A  \  B ) 
C_  A  ->  ( Rel  A  ->  Rel  ( A 
\  B ) ) )
31, 2ax-mp 5 1  |-  ( Rel 
A  ->  Rel  ( A 
\  B ) )
Colors of variables: wff setvar class
Syntax hints:    -> wi 4    \ cdif 3412    C_ wss 3415   Rel wrel 4857
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1679  ax-4 1692  ax-5 1768  ax-6 1815  ax-7 1861  ax-10 1925  ax-11 1930  ax-12 1943  ax-13 2101  ax-ext 2441
This theorem depends on definitions:  df-bi 190  df-an 377  df-tru 1457  df-ex 1674  df-nf 1678  df-sb 1808  df-clab 2448  df-cleq 2454  df-clel 2457  df-nfc 2591  df-v 3058  df-dif 3418  df-in 3422  df-ss 3429  df-rel 4859
This theorem is referenced by:  difopab  4984  relsdom  7601  opeldifid  28258  fundmpss  30455  relbigcup  30712
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