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Theorem rexxfrd 4606
 Description: Transfer universal quantification from a variable to another variable contained in expression . (Contributed by FL, 10-Apr-2007.) (Revised by Mario Carneiro, 15-Aug-2014.)
Hypotheses
Ref Expression
ralxfrd.1
ralxfrd.2
ralxfrd.3
Assertion
Ref Expression
rexxfrd
Distinct variable groups:   ,   ,,   ,   ,   ,,   ,
Allowed substitution hints:   ()   ()   ()   ()

Proof of Theorem rexxfrd
StepHypRef Expression
1 ralxfrd.1 . . . 4
2 ralxfrd.2 . . . 4
3 ralxfrd.3 . . . . 5
43notbid 292 . . . 4
51, 2, 4ralxfrd 4605 . . 3
65notbid 292 . 2
7 dfrex2 2855 . 2
8 dfrex2 2855 . 2
96, 7, 83bitr4g 288 1
 Colors of variables: wff setvar class Syntax hints:   wn 3   wi 4   wb 184   wa 367   wceq 1405   wcel 1842  wral 2754  wrex 2755 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1639  ax-4 1652  ax-5 1725  ax-6 1771  ax-7 1814  ax-10 1861  ax-11 1866  ax-12 1878  ax-13 2026  ax-ext 2380 This theorem depends on definitions:  df-bi 185  df-an 369  df-tru 1408  df-ex 1634  df-nf 1638  df-sb 1764  df-clab 2388  df-cleq 2394  df-clel 2397  df-nfc 2552  df-ral 2759  df-rex 2760  df-v 3061 This theorem is referenced by:  cmpfi  20201  elfm  20740  metucnOLD  21383  rlimcnp  23621  fargshiftfo  25055  rmoxfrdOLD  27806  rmoxfrd  27807  iunrdx  27861  dvh4dimat  34458  mapdcv  34680  elrfirn  34989
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