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Theorem riinn0 4405
Description: Relative intersection of a nonempty family. (Contributed by Stefan O'Rear, 3-Apr-2015.)
Assertion
Ref Expression
riinn0
Distinct variable groups:   ,   ,

Proof of Theorem riinn0
StepHypRef Expression
1 incom 3690 . 2
2 r19.2z 3918 . . . . 5
32ancoms 453 . . . 4
4 iinss 4381 . . . 4
53, 4syl 16 . . 3
6 df-ss 3489 . . 3
75, 6sylib 196 . 2
81, 7syl5eq 2510 1
Colors of variables: wff setvar class
Syntax hints:  ->wi 4  /\wa 369  =wceq 1395  =/=wne 2652  A.wral 2807  E.wrex 2808  i^icin 3474  C_wss 3475   c0 3784  |^|_ciin 4331
This theorem is referenced by:  riinrab  4406  riiner  7403  mreriincl  14995  riinopn  19417  alexsublem  20544  fnemeet1  30184
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1618  ax-4 1631  ax-5 1704  ax-6 1747  ax-7 1790  ax-10 1837  ax-11 1842  ax-12 1854  ax-13 1999  ax-ext 2435
This theorem depends on definitions:  df-bi 185  df-or 370  df-an 371  df-tru 1398  df-ex 1613  df-nf 1617  df-sb 1740  df-clab 2443  df-cleq 2449  df-clel 2452  df-nfc 2607  df-ne 2654  df-ral 2812  df-rex 2813  df-v 3111  df-dif 3478  df-in 3482  df-ss 3489  df-nul 3785  df-iin 4333
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