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

Theorem alxfr 4193
 Description: Transfer universal quantification from a variable to another variable contained in expression . (Contributed by NM, 18-Feb-2007.)
Hypothesis
Ref Expression
alxfr.1
Assertion
Ref Expression
alxfr
Distinct variable groups:   ,   ,   ,   ,
Allowed substitution hints:   ()   ()   ()   (,)

Proof of Theorem alxfr
StepHypRef Expression
1 alxfr.1 . . . . . . 7
21spcgv 2640 . . . . . 6
32com12 27 . . . . 5
43alimdv 1759 . . . 4
54com12 27 . . 3
65adantr 261 . 2
7 nfa1 1434 . . . . . 6
8 nfv 1421 . . . . . 6
9 sp 1401 . . . . . . 7
109, 1syl5ibrcom 146 . . . . . 6
117, 8, 10exlimd 1488 . . . . 5
1211alimdv 1759 . . . 4
1312com12 27 . . 3
1413adantl 262 . 2
156, 14impbid 120 1
 Colors of variables: wff set class Syntax hints:   wi 4   wa 97   wb 98  wal 1241   wceq 1243  wex 1381   wcel 1393 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-v 2559 This theorem is referenced by: (None)
 Copyright terms: Public domain W3C validator