NFE Home New Foundations Explorer < Previous   Next >
Nearby theorems
Mirrors  >  Home  >  NFE Home  >  Th. List  >  rexcom13 Unicode version

Theorem rexcom13 2773
Description: Swap 1st and 3rd restricted existential quantifiers. (Contributed by NM, 8-Apr-2015.)
Assertion
Ref Expression
rexcom13
Distinct variable groups:   ,,   ,,   ,,
Allowed substitution hints:   (,,)   ()   ()   ()

Proof of Theorem rexcom13
StepHypRef Expression
1 rexcom 2772 . 2
2 rexcom 2772 . . 3
32rexbii 2639 . 2
4 rexcom 2772 . 2
51, 3, 43bitri 262 1
Colors of variables: wff setvar class
Syntax hints:   wb 176  wrex 2615
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 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:  rexrot4  2774
  Copyright terms: Public domain W3C validator