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Theorem rexxfr2d 4673
 Description: Transfer universal quantification from a variable to another variable contained in expression . (Contributed by Mario Carneiro, 20-Aug-2014.) (Proof shortened by Mario Carneiro, 19-Nov-2016.)
Hypotheses
Ref Expression
ralxfr2d.1
ralxfr2d.2
ralxfr2d.3
Assertion
Ref Expression
rexxfr2d
Distinct variable groups:   ,   ,,   ,   ,   ,,   ,
Allowed substitution hints:   ()   ()   ()   ()   (,)

Proof of Theorem rexxfr2d
StepHypRef Expression
1 ralxfr2d.1 . . . 4
2 ralxfr2d.2 . . . 4
3 ralxfr2d.3 . . . . 5
43notbid 294 . . . 4
51, 2, 4ralxfr2d 4672 . . 3
65notbid 294 . 2
7 dfrex2 2908 . 2
8 dfrex2 2908 . 2
96, 7, 83bitr4g 288 1
 Colors of variables: wff setvar class Syntax hints:   wn 3   wi 4   wb 184   wa 369   wceq 1395   wcel 1819  wral 2807  wrex 2808 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1619  ax-4 1632  ax-5 1705  ax-6 1748  ax-7 1791  ax-10 1838  ax-11 1843  ax-12 1855  ax-13 2000  ax-ext 2435 This theorem depends on definitions:  df-bi 185  df-an 371  df-tru 1398  df-ex 1614  df-nf 1618  df-sb 1741  df-clab 2443  df-cleq 2449  df-clel 2452  df-nfc 2607  df-ral 2812  df-rex 2813  df-v 3111 This theorem is referenced by:  rexrn  6034  rexima  6152  cnpresti  19915  cnprest  19916  1stcrest  20079  subislly  20107  txrest  20257  trfil2  20513  met1stc  21149  metucn  21217  xrlimcnp  23423  esumlub  28223  esumfsup  28232  ptrest  30210  djhcvat42  37243
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