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

Theorem fvssunirng 5445
 Description: The result of a function value is always a subset of the union of the range, if the input is a set. (Contributed by Stefan O'Rear, 2-Nov-2014.) (Revised by Mario Carneiro, 24-May-2019.)
Assertion
Ref Expression
fvssunirng

Proof of Theorem fvssunirng
Dummy variable is distinct from all other variables.
StepHypRef Expression
1 vex 2693 . . . . 5
2 brelrng 4779 . . . . . 6
323exp 1181 . . . . 5
41, 3mpi 15 . . . 4
5 elssuni 3773 . . . 4
64, 5syl6 33 . . 3
76alrimiv 1847 . 2
8 fvss 5444 . 2
97, 8syl 14 1
 Colors of variables: wff set class Syntax hints:   wi 4  wal 1330   wcel 1481  cvv 2690   wss 3077  cuni 3745   class class class wbr 3938   crn 4549  cfv 5132 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-14 1493  ax-17 1507  ax-i9 1511  ax-ial 1515  ax-i5r 1516  ax-ext 2122  ax-sep 4055  ax-pow 4107  ax-pr 4140 This theorem depends on definitions:  df-bi 116  df-3an 965  df-tru 1335  df-nf 1438  df-sb 1737  df-eu 2003  df-mo 2004  df-clab 2127  df-cleq 2133  df-clel 2136  df-nfc 2271  df-ral 2422  df-rex 2423  df-v 2692  df-un 3081  df-in 3083  df-ss 3090  df-pw 3518  df-sn 3539  df-pr 3540  df-op 3542  df-uni 3746  df-br 3939  df-opab 3999  df-cnv 4556  df-dm 4558  df-rn 4559  df-iota 5097  df-fv 5140 This theorem is referenced by:  fvexg  5449  strfvssn  12040  xmetunirn  12586  mopnval  12670
 Copyright terms: Public domain W3C validator