Theorem relin1 3262

Description: The intersection with a relation is a relation.

Assertion

Ref	Expression
relin1	|- (Rel A -> Rel (A i^i B))

Proof of Theorem relin1

Step	Hyp	Ref	Expression
1		inss1 2230	. 2 |- (A i^i B) (_ A
2		relss 3246	. 2 |- ((A i^i B) (_ A -> (Rel A -> Rel (A i^i B)))
3	1, 2	ax-mp 7	1 |- (Rel A -> Rel (A i^i B))

Syntax hints:   -> wi 3   i^i cin 2046   (_ wss 2047  Rel wrel 3175

This theorem is referenced by:  inopab 3268  inxp 3269  cnvin 3456  funin 3566  sbthcl 4459  mapdom2lem 4493  infxpidmlem11 7562

This theorem was proved from axioms:  ax-1 4  ax-2 5  ax-3 6  ax-mp 7  ax-7 962  ax-gen 963  ax-8 964  ax-10 966  ax-12 968  ax-17 971  ax-4 973  ax-5o 975  ax-6o 978  ax-9o 1123  ax-10o 1140  ax-16 1210  ax-11o 1218  ax-ext 1459

This theorem depends on definitions:  df-bi 147  df-an 225  df-ex 981  df-sb 1172  df-clab 1464  df-cleq 1469  df-clel 1472  df-v 1812  df-in 2051  df-ss 2053  df-rel 3185

Copyright terms: Public domain