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Theorem rexxfr 4772
 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 2724 . 2
2 dfrex2 2724 . . 3
3 ralxfr.1 . . . 4
4 ralxfr.2 . . . 4
5 ralxfr.3 . . . . 5
65notbid 287 . . . 4
73, 4, 6ralxfr 4770 . . 3
82, 7xchbinxr 304 . 2
91, 8bitr4i 245 1
 Colors of variables: wff set class Syntax hints:   wn 3   wi 4   wb 178   wceq 1653   wcel 1727  wral 2711  wrex 2712 This theorem is referenced by:  infm3  9998  reeff1o  20394  moxfr  26771 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1556  ax-5 1567  ax-17 1627  ax-9 1668  ax-8 1689  ax-6 1746  ax-7 1751  ax-11 1763  ax-12 1953  ax-ext 2423 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 2429  df-cleq 2435  df-clel 2438  df-nfc 2567  df-ral 2716  df-rex 2717  df-v 2964
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