Metamath Proof Explorer < Previous   Next > Nearby theorems Mirrors  >  Home  >  MPE Home  >  Th. List  >  dfiin3g Structured version   Unicode version

Theorem dfiin3g 5126
 Description: Alternate definition of indexed intersection when is a set. (Contributed by Mario Carneiro, 31-Aug-2015.)
Assertion
Ref Expression
dfiin3g

Proof of Theorem dfiin3g
Dummy variable is distinct from all other variables.
StepHypRef Expression
1 dfiin2g 4126 . 2
2 eqid 2438 . . . 4
32rnmpt 5119 . . 3
43inteqi 4056 . 2
51, 4syl6eqr 2488 1
 Colors of variables: wff set class Syntax hints:   wi 4   wceq 1653   wcel 1726  cab 2424  wral 2707  wrex 2708  cint 4052  ciin 4096   cmpt 4269   crn 4882 This theorem is referenced by:  dfiin3  5128  riinint  5129  iinon  6605  cmpfi  17476 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1556  ax-5 1567  ax-17 1627  ax-9 1667  ax-8 1688  ax-14 1730  ax-6 1745  ax-7 1750  ax-11 1762  ax-12 1951  ax-ext 2419  ax-sep 4333  ax-nul 4341  ax-pr 4406 This theorem depends on definitions:  df-bi 179  df-or 361  df-an 362  df-3an 939  df-tru 1329  df-ex 1552  df-nf 1555  df-sb 1660  df-eu 2287  df-mo 2288  df-clab 2425  df-cleq 2431  df-clel 2434  df-nfc 2563  df-ne 2603  df-ral 2712  df-rex 2713  df-rab 2716  df-v 2960  df-dif 3325  df-un 3327  df-in 3329  df-ss 3336  df-nul 3631  df-if 3742  df-sn 3822  df-pr 3823  df-op 3825  df-int 4053  df-iin 4098  df-br 4216  df-opab 4270  df-mpt 4271  df-cnv 4889  df-dm 4891  df-rn 4892
 Copyright terms: Public domain W3C validator