Metamath Proof Explorer < Previous   Next > Nearby theorems Mirrors  >  Home  >  MPE Home  >  Th. List  >  suppss2OLD Unicode version

Theorem suppss2OLD 6530
 Description: Show that the support of a function is contained in a set. (Contributed by Mario Carneiro, 19-Dec-2014.) (Revised by Mario Carneiro, 22-Mar-2015.) Obsolete version of suppss2 6953 as of 28-May-2019. (New usage is discouraged.) (Proof modification is discouraged.)
Hypothesis
Ref Expression
suppss2OLD.n
Assertion
Ref Expression
suppss2OLD
Distinct variable groups:   ,   ,   ,   ,

Proof of Theorem suppss2OLD
StepHypRef Expression
1 eqid 2457 . . 3
21mptpreima 5505 . 2
3 eldifsni 4156 . . . . 5
4 eldif 3485 . . . . . . . 8
5 suppss2OLD.n . . . . . . . 8
64, 5sylan2br 476 . . . . . . 7
76expr 615 . . . . . 6
87necon1ad 2673 . . . . 5
93, 8syl5 32 . . . 4
1093impia 1193 . . 3
1110rabssdv 3579 . 2
122, 11syl5eqss 3547 1
 Colors of variables: wff setvar class Syntax hints:  -.wn 3  ->wi 4  /\wa 369  =wceq 1395  e.wcel 1818  =/=wne 2652  {crab 2811   cvv 3109  \cdif 3472  C_wss 3475  {csn 4029  e.cmpt 4510  'ccnv 5003  "`cima 5007 This theorem is referenced by:  cantnflem1dOLD  8151  cantnflem1OLD  8152  gsumzsplitOLD  16945  gsum2dOLD  17000  dprdfidOLD  17064  dprdfinvOLD  17066  dprdfaddOLD  17067  dmdprdsplitlemOLD  17085  dpjidclOLD  17114  psrbagaddclOLD  18021  psrbasOLD  18031  psrlidmOLD  18057  psrridmOLD  18059  mvridlemOLD  18075  mplcoe3OLD  18129  mplcoe2OLD  18133  mplbas2OLD  18135  evlslem4OLD  18173 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1618  ax-4 1631  ax-5 1704  ax-6 1747  ax-7 1790  ax-9 1822  ax-10 1837  ax-11 1842  ax-12 1854  ax-13 1999  ax-ext 2435  ax-sep 4573  ax-nul 4581  ax-pr 4691 This theorem depends on definitions:  df-bi 185  df-or 370  df-an 371  df-3an 975  df-tru 1398  df-ex 1613  df-nf 1617  df-sb 1740  df-eu 2286  df-mo 2287  df-clab 2443  df-cleq 2449  df-clel 2452  df-nfc 2607  df-ne 2654  df-ral 2812  df-rex 2813  df-rab 2816  df-v 3111  df-dif 3478  df-un 3480  df-in 3482  df-ss 3489  df-nul 3785  df-if 3942  df-sn 4030  df-pr 4032  df-op 4036  df-br 4453  df-opab 4511  df-mpt 4512  df-xp 5010  df-rel 5011  df-cnv 5012  df-dm 5014  df-rn 5015  df-res 5016  df-ima 5017
 Copyright terms: Public domain W3C validator