Mathbox for Frédéric Liné < Previous   Next > Nearby theorems Mirrors  >  Home  >  MPE Home  >  Th. List  >   Mathboxes  >  trdom2 Unicode version

Theorem trdom2 25391
 Description: The domain of a right translation. The term is a constant: is not present. (Contributed by FL, 21-Jun-2010.)
Hypotheses
Ref Expression
trfun.2
trinv.1
Assertion
Ref Expression
trdom2
Distinct variable groups:   ,   ,   ,
Allowed substitution hint:   ()

Proof of Theorem trdom2
StepHypRef Expression
1 ovex 5883 . . . 4
21a1i 10 . . 3
32ralrimiva 2626 . 2
4 trfun.2 . . 3
54cmpdom 25143 . 2
63, 5sylib 188 1
 Colors of variables: wff set class Syntax hints:   wi 4   wa 358   wceq 1623   wcel 1684  wral 2543  cvv 2788   cmpt 4077   cdm 4689   crn 4690  (class class class)co 5858  cgr 20853 This theorem is referenced by:  imtr  25398 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1533  ax-5 1544  ax-17 1603  ax-9 1635  ax-8 1643  ax-14 1688  ax-6 1703  ax-7 1708  ax-11 1715  ax-12 1866  ax-ext 2264  ax-sep 4141  ax-nul 4149  ax-pr 4214 This theorem depends on definitions:  df-bi 177  df-or 359  df-an 360  df-3an 936  df-tru 1310  df-ex 1529  df-nf 1532  df-sb 1630  df-eu 2147  df-mo 2148  df-clab 2270  df-cleq 2276  df-clel 2279  df-nfc 2408  df-ne 2448  df-ral 2548  df-rex 2549  df-rab 2552  df-v 2790  df-sbc 2992  df-dif 3155  df-un 3157  df-in 3159  df-ss 3166  df-nul 3456  df-if 3566  df-sn 3646  df-pr 3647  df-op 3649  df-uni 3828  df-br 4024  df-opab 4078  df-mpt 4079  df-id 4309  df-xp 4695  df-rel 4696  df-cnv 4697  df-co 4698  df-dm 4699  df-iota 5219  df-fun 5257  df-fn 5258  df-fv 5263  df-ov 5861
 Copyright terms: Public domain W3C validator