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Theorem rexxfr2d 4732
 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 286 . . . 4
51, 2, 4ralxfr2d 4731 . . 3
65notbid 286 . 2
7 dfrex2 2710 . 2
8 dfrex2 2710 . 2
96, 7, 83bitr4g 280 1
 Colors of variables: wff set class Syntax hints:   wn 3   wi 4   wb 177   wa 359   wceq 1652   wcel 1725  wral 2697  wrex 2698 This theorem is referenced by:  rexrn  5864  rexima  5969  cnpresti  17344  cnprest  17345  1stcrest  17508  subislly  17536  txrest  17655  trfil2  17911  met1stc  18543  xrlimcnp  20799  esumlub  24444  esumfsup  24452  djhcvat42  32140 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1555  ax-5 1566  ax-17 1626  ax-9 1666  ax-8 1687  ax-6 1744  ax-7 1749  ax-11 1761  ax-12 1950  ax-ext 2416 This theorem depends on definitions:  df-bi 178  df-or 360  df-an 361  df-tru 1328  df-ex 1551  df-nf 1554  df-sb 1659  df-clab 2422  df-cleq 2428  df-clel 2431  df-nfc 2560  df-ral 2702  df-rex 2703  df-v 2950
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