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Theorem reliin 5117
 Description: An indexed intersection is a relation if at least one of the member of the indexed family is a relation. (Contributed by NM, 8-Mar-2014.)
Assertion
Ref Expression
reliin

Proof of Theorem reliin
StepHypRef Expression
1 iinss 4371 . 2
2 df-rel 5001 . . 3
32rexbii 2960 . 2
4 df-rel 5001 . 2
51, 3, 43imtr4i 266 1
 Colors of variables: wff setvar class Syntax hints:   wi 4  wrex 2810  cvv 3108   wss 3471  ciin 4321   cxp 4992   wrel 4999 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1596  ax-4 1607  ax-5 1675  ax-6 1714  ax-7 1734  ax-10 1781  ax-11 1786  ax-12 1798  ax-13 1963  ax-ext 2440 This theorem depends on definitions:  df-bi 185  df-an 371  df-tru 1377  df-ex 1592  df-nf 1595  df-sb 1707  df-clab 2448  df-cleq 2454  df-clel 2457  df-nfc 2612  df-ral 2814  df-rex 2815  df-v 3110  df-in 3478  df-ss 3485  df-iin 4323  df-rel 5001 This theorem is referenced by:  relint  5119  xpiindi  5131  dibglbN  35840  dihglbcpreN  35974
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