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Theorem rexcomf 2867
 Description: Commutation of restricted quantifiers. (Contributed by Mario Carneiro, 14-Oct-2016.)
Hypotheses
Ref Expression
ralcomf.1
ralcomf.2
Assertion
Ref Expression
rexcomf
Distinct variable group:   ,
Allowed substitution hints:   (,)   (,)   (,)

Proof of Theorem rexcomf
StepHypRef Expression
1 ancom 438 . . . . 5
21anbi1i 677 . . . 4
322exbii 1593 . . 3
4 excom 1756 . . 3
53, 4bitri 241 . 2
6 ralcomf.1 . . 3
76r2exf 2741 . 2
8 ralcomf.2 . . 3
98r2exf 2741 . 2
105, 7, 93bitr4i 269 1
 Colors of variables: wff set class Syntax hints:   wb 177   wa 359  wex 1550   wcel 1725  wnfc 2559  wrex 2706 This theorem is referenced by:  rexcom  2869  rexcom4f  23966 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 2417 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-cleq 2429  df-clel 2432  df-nfc 2561  df-rex 2711
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