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Theorem reldif 4805
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 3303 . 2  |-  ( A 
\  B )  C_  A
2 relss 4775 . 2  |-  ( ( A  \  B ) 
C_  A  ->  ( Rel  A  ->  Rel  ( A 
\  B ) ) )
31, 2ax-mp 8 1  |-  ( Rel 
A  ->  Rel  ( A 
\  B ) )
Colors of variables: wff set class
Syntax hints:    -> wi 4    \ cdif 3149    C_ wss 3152   Rel wrel 4694
This theorem is referenced by:  difopab  4817  relsdom  6870  fundmpss  24122  relbigcup  24437
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1533  ax-5 1544  ax-17 1603  ax-9 1635  ax-8 1643  ax-6 1703  ax-7 1708  ax-11 1715  ax-12 1866  ax-ext 2264
This theorem depends on definitions:  df-bi 177  df-or 359  df-an 360  df-tru 1310  df-ex 1529  df-nf 1532  df-sb 1630  df-clab 2270  df-cleq 2276  df-clel 2279  df-nfc 2408  df-v 2790  df-dif 3155  df-in 3159  df-ss 3166  df-rel 4696
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