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Theorem rexxfr 4619
 Description: Transfer existence from a variable to another variable contained in expression . (Contributed by NM, 10-Jun-2005.) (Revised by Mario Carneiro, 15-Aug-2014.)
Hypotheses
Ref Expression
ralxfr.1
ralxfr.2
ralxfr.3
Assertion
Ref Expression
rexxfr
Distinct variable groups:   ,   ,   ,   ,,   ,
Allowed substitution hints:   ()   ()   ()   ()

Proof of Theorem rexxfr
StepHypRef Expression
1 dfrex2 2837 . 2
2 dfrex2 2837 . . 3
3 ralxfr.1 . . . 4
4 ralxfr.2 . . . 4
5 ralxfr.3 . . . . 5
65notbid 296 . . . 4
73, 4, 6ralxfr 4617 . . 3
82, 7xchbinxr 313 . 2
91, 8bitr4i 256 1
 Colors of variables: wff setvar class Syntax hints:   wn 3   wi 4   wb 188   wceq 1443   wcel 1886  wral 2736  wrex 2737 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1668  ax-4 1681  ax-5 1757  ax-6 1804  ax-7 1850  ax-10 1914  ax-11 1919  ax-12 1932  ax-13 2090  ax-ext 2430 This theorem depends on definitions:  df-bi 189  df-an 373  df-tru 1446  df-ex 1663  df-nf 1667  df-sb 1797  df-clab 2437  df-cleq 2443  df-clel 2446  df-nfc 2580  df-ral 2741  df-rex 2742  df-v 3046 This theorem is referenced by:  infm3  10565  reeff1o  23395  moxfr  35528
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