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Theorem relint 4962
 Description: The intersection of a class is a relation if at least one member is a relation. (Contributed by NM, 8-Mar-2014.)
Assertion
Ref Expression
relint
Distinct variable group:   ,

Proof of Theorem relint
StepHypRef Expression
1 reliin 4960 . 2
2 intiin 4323 . . 3
32releqi 4923 . 2
41, 3sylibr 217 1
 Colors of variables: wff setvar class Syntax hints:   wi 4  wrex 2757  cint 4226  ciin 4270   wrel 4844 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1677  ax-4 1690  ax-5 1766  ax-6 1813  ax-7 1859  ax-10 1932  ax-11 1937  ax-12 1950  ax-13 2104  ax-ext 2451 This theorem depends on definitions:  df-bi 190  df-an 378  df-tru 1455  df-ex 1672  df-nf 1676  df-sb 1806  df-clab 2458  df-cleq 2464  df-clel 2467  df-nfc 2601  df-ral 2761  df-rex 2762  df-v 3033  df-in 3397  df-ss 3404  df-int 4227  df-iin 4272  df-rel 4846 This theorem is referenced by:  clrellem  36300
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