New Foundations Explorer < Previous   Next > Nearby theorems Mirrors  >  Home  >  NFE Home  >  Th. List  >  rexcomf Unicode version

Theorem rexcomf 2770
 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 437 . . . . 5
21anbi1i 676 . . . 4
322exbii 1583 . . 3
4 excom 1741 . . 3
53, 4bitri 240 . 2
6 ralcomf.1 . . 3
76r2exf 2650 . 2
8 ralcomf.2 . . 3
98r2exf 2650 . 2
105, 7, 93bitr4i 268 1
 Colors of variables: wff setvar class Syntax hints:   wb 176   wa 358  wex 1541   wcel 1710  wnfc 2476  wrex 2615 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1546  ax-5 1557  ax-17 1616  ax-9 1654  ax-8 1675  ax-6 1729  ax-7 1734  ax-11 1746  ax-12 1925  ax-ext 2334 This theorem depends on definitions:  df-bi 177  df-or 359  df-an 360  df-tru 1319  df-ex 1542  df-nf 1545  df-sb 1649  df-cleq 2346  df-clel 2349  df-nfc 2478  df-rex 2620 This theorem is referenced by:  rexcom  2772
 Copyright terms: Public domain W3C validator