Intuitionistic Logic Explorer < Previous   Next > Nearby theorems Mirrors  >  Home  >  ILE Home  >  Th. List  >  intssunim Unicode version

Theorem intssunim 3802
 Description: The intersection of an inhabited set is a subclass of its union. (Contributed by NM, 29-Jul-2006.)
Assertion
Ref Expression
intssunim
Distinct variable group:   ,

Proof of Theorem intssunim
Dummy variable is distinct from all other variables.
StepHypRef Expression
1 r19.2m 3455 . . . 4
21ex 114 . . 3
3 vex 2693 . . . 4
43elint2 3787 . . 3
5 eluni2 3749 . . 3
62, 4, 53imtr4g 204 . 2
76ssrdv 3109 1
 Colors of variables: wff set class Syntax hints:   wi 4  wex 1469   wcel 1481  wral 2417  wrex 2418   wss 3077  cuni 3745  cint 3780 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 105  ax-ia2 106  ax-ia3 107  ax-io 699  ax-5 1424  ax-7 1425  ax-gen 1426  ax-ie1 1470  ax-ie2 1471  ax-8 1483  ax-10 1484  ax-11 1485  ax-i12 1486  ax-bndl 1487  ax-4 1488  ax-17 1507  ax-i9 1511  ax-ial 1515  ax-i5r 1516  ax-ext 2122 This theorem depends on definitions:  df-bi 116  df-tru 1335  df-nf 1438  df-sb 1737  df-clab 2127  df-cleq 2133  df-clel 2136  df-nfc 2271  df-ral 2422  df-rex 2423  df-v 2692  df-in 3083  df-ss 3090  df-uni 3746  df-int 3781 This theorem is referenced by:  intssuni2m  3804
 Copyright terms: Public domain W3C validator