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Theorem riinn0 4372
 Description: Relative intersection of a nonempty family. (Contributed by Stefan O'Rear, 3-Apr-2015.)
Assertion
Ref Expression
riinn0
Distinct variable groups:   ,   ,
Allowed substitution hint:   ()

Proof of Theorem riinn0
StepHypRef Expression
1 incom 3656 . 2
2 r19.2z 3887 . . . . 5
32ancoms 455 . . . 4
4 iinss 4348 . . . 4
53, 4syl 17 . . 3
6 df-ss 3451 . . 3
75, 6sylib 200 . 2
81, 7syl5eq 2476 1
 Colors of variables: wff setvar class Syntax hints:   wi 4   wa 371   wceq 1438   wne 2619  wral 2776  wrex 2777   cin 3436   wss 3437  c0 3762  ciin 4298 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1666  ax-4 1679  ax-5 1749  ax-6 1795  ax-7 1840  ax-10 1888  ax-11 1893  ax-12 1906  ax-13 2054  ax-ext 2401 This theorem depends on definitions:  df-bi 189  df-or 372  df-an 373  df-tru 1441  df-ex 1661  df-nf 1665  df-sb 1788  df-clab 2409  df-cleq 2415  df-clel 2418  df-nfc 2573  df-ne 2621  df-ral 2781  df-rex 2782  df-v 3084  df-dif 3440  df-in 3444  df-ss 3451  df-nul 3763  df-iin 4300 This theorem is referenced by:  riinrab  4373  riiner  7442  mreriincl  15497  riinopn  19930  alexsublem  21051  fnemeet1  31021
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