Metamath Proof Explorer < Previous   Next > Nearby theorems Mirrors  >  Home  >  MPE Home  >  Th. List  >  riin0 Structured version   Visualization version   Unicode version

Theorem riin0 4352
 Description: Relative intersection of an empty family. (Contributed by Stefan O'Rear, 3-Apr-2015.)
Assertion
Ref Expression
riin0
Distinct variable groups:   ,   ,
Allowed substitution hint:   ()

Proof of Theorem riin0
StepHypRef Expression
1 iineq1 4293 . . 3
21ineq2d 3634 . 2
3 0iin 4336 . . . 4
43ineq2i 3631 . . 3
5 inv1 3761 . . 3
64, 5eqtri 2473 . 2
72, 6syl6eq 2501 1
 Colors of variables: wff setvar class Syntax hints:   wi 4   wceq 1444  cvv 3045   cin 3403  c0 3731  ciin 4279 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1669  ax-4 1682  ax-5 1758  ax-6 1805  ax-7 1851  ax-10 1915  ax-11 1920  ax-12 1933  ax-13 2091  ax-ext 2431 This theorem depends on definitions:  df-bi 189  df-an 373  df-tru 1447  df-ex 1664  df-nf 1668  df-sb 1798  df-clab 2438  df-cleq 2444  df-clel 2447  df-nfc 2581  df-ral 2742  df-v 3047  df-dif 3407  df-in 3411  df-ss 3418  df-nul 3732  df-iin 4281 This theorem is referenced by:  riinrab  4354  riiner  7436  mreriincl  15504  riinopn  19938  riincld  20059  fnemeet2  31023  pmapglb2N  33336  pmapglb2xN  33337
 Copyright terms: Public domain W3C validator