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Theorem alxfr 4665
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:   ,   ,   ,   ,

Proof of Theorem alxfr
StepHypRef Expression
1 alxfr.1 . . . . . . 7
21spcgv 3194 . . . . . 6
32com12 31 . . . . 5
43alimdv 1709 . . . 4
54com12 31 . . 3
65adantr 465 . 2
7 nfa1 1897 . . . . . 6
8 nfv 1707 . . . . . 6
9 sp 1859 . . . . . . 7
109, 1syl5ibrcom 222 . . . . . 6
117, 8, 10exlimd 1914 . . . . 5
1211alimdv 1709 . . . 4
1312com12 31 . . 3
1413adantl 466 . 2
156, 14impbid 191 1
Colors of variables: wff setvar class
Syntax hints:  ->wi 4  <->wb 184  /\wa 369  A.wal 1393  =wceq 1395  E.wex 1612  e.wcel 1818
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-10 1837  ax-11 1842  ax-12 1854  ax-13 1999  ax-ext 2435
This theorem depends on definitions:  df-bi 185  df-an 371  df-tru 1398  df-ex 1613  df-nf 1617  df-sb 1740  df-clab 2443  df-cleq 2449  df-clel 2452  df-nfc 2607  df-v 3111
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