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Theorem bj-1nel0 32541
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 6956 . . . 4  |-  1o  =/=  (/)
21neii 2624 . . 3  |-  -.  1o  =  (/)
3 elsni 3923 . . 3  |-  ( 1o  e.  { (/) }  ->  1o  =  (/) )
42, 3mto 176 . 2  |-  -.  1o  e.  { (/) }
54nelir 2729 1  |-  1o  e/  {
(/) }
Colors of variables: wff setvar class
Syntax hints:    = wceq 1369    e. wcel 1756    e/ wnel 2621   (/)c0 3658   {csn 3898   1oc1o 6934
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1591  ax-4 1602  ax-5 1670  ax-6 1708  ax-7 1728  ax-10 1775  ax-11 1780  ax-12 1792  ax-13 1943  ax-ext 2423  ax-nul 4442
This theorem depends on definitions:  df-bi 185  df-or 370  df-an 371  df-tru 1372  df-ex 1587  df-nf 1590  df-sb 1701  df-clab 2430  df-cleq 2436  df-clel 2439  df-nfc 2577  df-ne 2622  df-nel 2623  df-v 2995  df-dif 3352  df-un 3354  df-nul 3659  df-sn 3899  df-suc 4746  df-1o 6941
This theorem is referenced by: (None)
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