Metamath Proof Explorer < Previous   Next > Nearby theorems Mirrors  >  Home  >  MPE Home  >  Th. List  >  eldifpr Unicode version

Theorem eldifpr 4046
 Description: Membership in a set with two elements removed. Similar to eldifsn 4155 and eldiftp 4072. (Contributed by Mario Carneiro, 18-Jul-2017.)
Assertion
Ref Expression
eldifpr

Proof of Theorem eldifpr
StepHypRef Expression
1 elprg 4045 . . . . 5
21notbid 294 . . . 4
3 neanior 2782 . . . 4
42, 3syl6bbr 263 . . 3
54pm5.32i 637 . 2
6 eldif 3485 . 2
7 3anass 977 . 2
85, 6, 73bitr4i 277 1
 Colors of variables: wff setvar class Syntax hints:  -.wn 3  <->wb 184  \/wo 368  /\wa 369  /\w3a 973  =wceq 1395  e.wcel 1818  =/=wne 2652  \cdif 3472  {cpr 4031 This theorem is referenced by:  logbcl  28013  logbid1  28014  rnlogbval  28016  relogbcl  28018  logb1  28019  nnlogbexp  28020  rexdifpr  32300  elogb  33169 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1618  ax-4 1631  ax-5 1704  ax-6 1747  ax-7 1790  ax-10 1837  ax-11 1842  ax-12 1854  ax-13 1999  ax-ext 2435 This theorem depends on definitions:  df-bi 185  df-or 370  df-an 371  df-3an 975  df-tru 1398  df-ex 1613  df-nf 1617  df-sb 1740  df-clab 2443  df-cleq 2449  df-clel 2452  df-nfc 2607  df-ne 2654  df-v 3111  df-dif 3478  df-un 3480  df-sn 4030  df-pr 4032
 Copyright terms: Public domain W3C validator