Users' Mathboxes Mathbox for BJ < Previous   Next >
Nearby theorems
Mirrors  >  Home  >  MPE Home  >  Th. List  >   Mathboxes  >  bj-1nel0 Structured version   Unicode version

Theorem bj-1nel0 34858
Description:  1o does not belong to  { (/) }. (Contributed by BJ, 6-Apr-2019.)
Assertion
Ref Expression
bj-1nel0  |-  1o  e/  {
(/) }

Proof of Theorem bj-1nel0
StepHypRef Expression
1 1n0 7063 . . . 4  |-  1o  =/=  (/)
21neii 2581 . . 3  |-  -.  1o  =  (/)
3 elsni 3969 . . 3  |-  ( 1o  e.  { (/) }  ->  1o  =  (/) )
42, 3mto 176 . 2  |-  -.  1o  e.  { (/) }
54nelir 2718 1  |-  1o  e/  {
(/) }
Colors of variables: wff setvar class
Syntax hints:    = wceq 1399    e. wcel 1826    e/ wnel 2578   (/)c0 3711   {csn 3944   1oc1o 7041
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1626  ax-4 1639  ax-5 1712  ax-6 1755  ax-7 1798  ax-10 1845  ax-11 1850  ax-12 1862  ax-13 2006  ax-ext 2360  ax-nul 4496
This theorem depends on definitions:  df-bi 185  df-or 368  df-an 369  df-tru 1402  df-ex 1621  df-nf 1625  df-sb 1748  df-clab 2368  df-cleq 2374  df-clel 2377  df-nfc 2532  df-ne 2579  df-nel 2580  df-v 3036  df-dif 3392  df-un 3394  df-nul 3712  df-sn 3945  df-suc 4798  df-1o 7048
This theorem is referenced by: (None)
  Copyright terms: Public domain W3C validator