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

Theorem suppval 6920
 Description: The value of the operation constructing the support of a function. (Contributed by AV, 31-Mar-2019.) (Revised by AV, 6-Apr-2019.)
Assertion
Ref Expression
suppval
Distinct variable groups:   ,   ,

Proof of Theorem suppval
Dummy variables are mutually distinct and distinct from all other variables.
StepHypRef Expression
1 df-supp 6919 . . 3
21a1i 11 . 2
3 dmeq 5208 . . . . 5
43adantr 465 . . . 4
5 imaeq1 5337 . . . . . 6
65adantr 465 . . . . 5
7 sneq 4039 . . . . . 6
87adantl 466 . . . . 5
96, 8neeq12d 2736 . . . 4
104, 9rabeqbidv 3104 . . 3
 Colors of variables: wff setvar class Syntax hints:  ->wi 4  /\wa 369  =wceq 1395  e.wcel 1818  =/=wne 2652  {crab 2811   cvv 3109  {csn 4029  domcdm 5004  "cima 5007  (class class class)co 6296  e.cmpt2 6298   csupp 6918 This theorem is referenced by:  suppvalbr  6922  supp0  6923  suppval1  6924  suppssdm  6931  suppsnop  6932  ressuppss  6938  ressuppssdif  6940 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-8 1820  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  ax-un 6592 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-sbc 3328  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-uni 4250  df-br 4453  df-opab 4511  df-id 4800  df-xp 5010  df-rel 5011  df-cnv 5012  df-co 5013  df-dm 5014  df-rn 5015  df-res 5016  df-ima 5017  df-iota 5556  df-fun 5595  df-fv 5601  df-ov 6299  df-oprab 6300  df-mpt2 6301  df-supp 6919