Theorem reldif 2492

Description: A difference cutting down a relation is a relation.

Assertion

Ref	Expression
reldif	|- (Rel A -> Rel (A \ B))

Proof of Theorem reldif

Step	Hyp	Ref	Expression
1		difss 1596	. 2 |- (A \ B) (_ A
2		ssrel 2479	. 2 |- ((A \ B) (_ A -> (Rel A -> Rel (A \ B)))
3	1, 2	ax-mp 6	1 |- (Rel A -> Rel (A \ B))

Syntax hints:   -> wi 2   \ cdif 1484   (_ wss 1487  Rel wrel 2415

This theorem is referenced by:  relsdom 3279

This theorem was proved from axioms:  ax-1 3  ax-2 4  ax-3 5  ax-mp 6  ax-4 673  ax-5 674  ax-6 675  ax-7 676  ax-gen 677  ax-8 798  ax-9 799  ax-10 800  ax-11 801  ax-12 802  ax-16 922  ax-17 925  ax-ext 1074

This theorem depends on definitions:  df-bi 128  df-an 198  df-ex 679  df-sb 853  df-clab 1093  df-cleq 1097  df-clel 1099  df-v 1349  df-dif 1489  df-in 1491  df-ss 1492  df-rel 2425

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