Mathbox for Alexander van der Vekens < Previous   Next > Nearby theorems Mirrors  >  Home  >  MPE Home  >  Th. List  >   Mathboxes  >  ralnralall Structured version   Unicode version

Theorem ralnralall 32128
 Description: A contradiction concerning restricted generalization for a nonempty set implies anything. (Contributed by Alexander van der Vekens, 4-Sep-2018.)
Assertion
Ref Expression
ralnralall
Distinct variable group:   ,
Allowed substitution hints:   ()   ()

Proof of Theorem ralnralall
StepHypRef Expression
1 r19.26 2968 . 2
2 pm3.24 880 . . . . 5
32bifal 1394 . . . 4
43ralbii 2872 . . 3
5 r19.3rzv 3904 . . . 4
6 falim 1395 . . . 4
75, 6syl6bir 229 . . 3
84, 7syl5bi 217 . 2
91, 8syl5bir 218 1
 Colors of variables: wff setvar class Syntax hints:   wn 3   wi 4   wa 369   wfal 1386   wne 2636  wral 2791  c0 3767 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1603  ax-4 1616  ax-5 1689  ax-6 1732  ax-7 1774  ax-10 1821  ax-11 1826  ax-12 1838  ax-13 1983  ax-ext 2419 This theorem depends on definitions:  df-bi 185  df-or 370  df-an 371  df-tru 1384  df-fal 1387  df-ex 1598  df-nf 1602  df-sb 1725  df-clab 2427  df-cleq 2433  df-clel 2436  df-nfc 2591  df-ne 2638  df-ral 2796  df-v 3095  df-dif 3461  df-nul 3768 This theorem is referenced by: (None)
 Copyright terms: Public domain W3C validator