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

Theorem ralxfr 4198
 Description: Transfer universal quantification from a variable to another variable contained in expression . (Contributed by NM, 10-Jun-2005.) (Revised by Mario Carneiro, 15-Aug-2014.)
Hypotheses
Ref Expression
ralxfr.1
ralxfr.2
ralxfr.3
Assertion
Ref Expression
ralxfr
Distinct variable groups:   ,   ,   ,   ,,   ,
Allowed substitution hints:   ()   ()   ()   ()

Proof of Theorem ralxfr
StepHypRef Expression
1 ralxfr.1 . . . 4
21adantl 262 . . 3
3 ralxfr.2 . . . 4
43adantl 262 . . 3
5 ralxfr.3 . . . 4
65adantl 262 . . 3
72, 4, 6ralxfrd 4194 . 2
87trud 1252 1
 Colors of variables: wff set class Syntax hints:   wi 4   wb 98   wceq 1243   wtru 1244   wcel 1393  wral 2306  wrex 2307 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 99  ax-ia2 100  ax-ia3 101  ax-io 630  ax-5 1336  ax-7 1337  ax-gen 1338  ax-ie1 1382  ax-ie2 1383  ax-8 1395  ax-10 1396  ax-11 1397  ax-i12 1398  ax-bndl 1399  ax-4 1400  ax-17 1419  ax-i9 1423  ax-ial 1427  ax-i5r 1428  ax-ext 2022 This theorem depends on definitions:  df-bi 110  df-tru 1246  df-nf 1350  df-sb 1646  df-clab 2027  df-cleq 2033  df-clel 2036  df-nfc 2167  df-ral 2311  df-rex 2312  df-v 2559 This theorem is referenced by: (None)
 Copyright terms: Public domain W3C validator