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Theorem riinn0 4157
 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 3525 . 2
2 r19.2z 3709 . . . . 5
32ancoms 440 . . . 4
4 iinss 4134 . . . 4
53, 4syl 16 . . 3
6 df-ss 3326 . . 3
75, 6sylib 189 . 2
81, 7syl5eq 2479 1
 Colors of variables: wff set class Syntax hints:   wi 4   wa 359   wceq 1652   wne 2598  wral 2697  wrex 2698   cin 3311   wss 3312  c0 3620  ciin 4086 This theorem is referenced by:  riinrab  4158  riiner  6969  mreriincl  13813  riinopn  16971  alexsublem  18065  fnemeet1  26349 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1555  ax-5 1566  ax-17 1626  ax-9 1666  ax-8 1687  ax-6 1744  ax-7 1749  ax-11 1761  ax-12 1950  ax-ext 2416 This theorem depends on definitions:  df-bi 178  df-or 360  df-an 361  df-tru 1328  df-ex 1551  df-nf 1554  df-sb 1659  df-clab 2422  df-cleq 2428  df-clel 2431  df-nfc 2560  df-ne 2600  df-ral 2702  df-rex 2703  df-v 2950  df-dif 3315  df-in 3319  df-ss 3326  df-nul 3621  df-iin 4088
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