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Theorem rexxfrd 4740
 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 287 . . . 4
51, 2, 4ralxfrd 4739 . . 3
65notbid 287 . 2
7 dfrex2 2720 . 2
8 dfrex2 2720 . 2
96, 7, 83bitr4g 281 1
 Colors of variables: wff set class Syntax hints:   wn 3   wi 4   wb 178   wa 360   wceq 1653   wcel 1726  wral 2707  wrex 2708 This theorem is referenced by:  cmpfi  17473  elfm  17981  metucnOLD  18620  metucn  18621  rlimcnp  20806  fargshiftfo  21627  rmoxfrdOLD  23981  rmoxfrd  23982  iunrdx  24016  elrfirn  26751  dvh4dimat  32298  mapdcv  32520 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1556  ax-5 1567  ax-17 1627  ax-9 1667  ax-8 1688  ax-6 1745  ax-7 1750  ax-11 1762  ax-12 1951  ax-ext 2419 This theorem depends on definitions:  df-bi 179  df-or 361  df-an 362  df-tru 1329  df-ex 1552  df-nf 1555  df-sb 1660  df-clab 2425  df-cleq 2431  df-clel 2434  df-nfc 2563  df-ral 2712  df-rex 2713  df-v 2960
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