Theorem relin1 3257

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 2226	. 2 |- (A i^i B) (_ A
2		relss 3241	. 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 2042   (_ wss 2043  Rel wrel 3170

This theorem is referenced by:  inopab 3263  inxp 3264  cnvin 3448  funin 3558  sbthcl 4445  mapdom2lem 4479  infxpidmlem11 7513

This theorem was proved from axioms:  ax-1 4  ax-2 5  ax-3 6  ax-mp 7  ax-7 960  ax-gen 961  ax-8 962  ax-10 964  ax-12 966  ax-17 969  ax-4 971  ax-5o 973  ax-6o 976  ax-9o 1121  ax-10o 1138  ax-16 1208  ax-11o 1216  ax-ext 1457

This theorem depends on definitions:  df-bi 147  df-an 225  df-ex 979  df-sb 1170  df-clab 1462  df-cleq 1467  df-clel 1470  df-v 1808  df-in 2047  df-ss 2049  df-rel 3180

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