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

Theorem iinvdif 4374
 Description: The indexed intersection of a complement. (Contributed by Gérard Lang, 5-Aug-2018.)
Assertion
Ref Expression
iinvdif
Distinct variable group:   ,
Allowed substitution hint:   ()

Proof of Theorem iinvdif
StepHypRef Expression
1 dif0 3871 . . . 4
2 0iun 4359 . . . . 5
32difeq2i 3586 . . . 4
4 0iin 4360 . . . 4
51, 3, 43eqtr4ri 2469 . . 3
6 iineq1 4317 . . 3
7 iuneq1 4316 . . . 4
87difeq2d 3589 . . 3
95, 6, 83eqtr4a 2496 . 2
10 iindif2 4371 . 2
119, 10pm2.61ine 2744 1
 Colors of variables: wff setvar class Syntax hints:   wceq 1437  cvv 3087   cdif 3439  c0 3767  ciun 4302  ciin 4303 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1665  ax-4 1678  ax-5 1751  ax-6 1797  ax-7 1841  ax-10 1889  ax-11 1894  ax-12 1907  ax-13 2055  ax-ext 2407 This theorem depends on definitions:  df-bi 188  df-or 371  df-an 372  df-tru 1440  df-ex 1660  df-nf 1664  df-sb 1790  df-clab 2415  df-cleq 2421  df-clel 2424  df-nfc 2579  df-ne 2627  df-ral 2787  df-rex 2788  df-rab 2791  df-v 3089  df-dif 3445  df-in 3449  df-ss 3456  df-nul 3768  df-iun 4304  df-iin 4305 This theorem is referenced by: (None)
 Copyright terms: Public domain W3C validator