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Theorem reldif 4821
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 3316 . 2  |-  ( A 
\  B )  C_  A
2 relss 4791 . 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 3162    C_ wss 3165   Rel wrel 4710
This theorem is referenced by:  difopab  4833  relsdom  6886  fundmpss  24193  relbigcup  24508
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-dif 3168  df-in 3172  df-ss 3179  df-rel 4712
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