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

Theorem rnoprab 6385
 Description: The range of an operation class abstraction. (Contributed by NM, 30-Aug-2004.) (Revised by David Abernethy, 19-Apr-2013.)
Assertion
Ref Expression
rnoprab
Distinct variable groups:   ,   ,

Proof of Theorem rnoprab
Dummy variable is distinct from all other variables.
StepHypRef Expression
1 dfoprab2 6343 . . 3
21rneqi 5234 . 2
3 rnopab 5252 . 2
4 exrot3 1852 . . . 4
5 opex 4716 . . . . . . 7
65isseti 3115 . . . . . 6
7 19.41v 1771 . . . . . 6
86, 7mpbiran 918 . . . . 5
982exbii 1668 . . . 4
104, 9bitri 249 . . 3
1110abbii 2591 . 2
122, 3, 113eqtri 2490 1
 Colors of variables: wff setvar class Syntax hints:  /\wa 369  =wceq 1395  E.wex 1612  {cab 2442  <.cop 4035  {copab 4509  rancrn 5005  {coprab 6297 This theorem is referenced by:  rnoprab2  6386  elrnmpt2res  6416  ellines  29802 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-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-cnv 5012  df-dm 5014  df-rn 5015  df-oprab 6300
 Copyright terms: Public domain W3C validator