Theorem bj-1nel0 32941

Description: 1o does not belong to { (/) }. (Contributed by BJ, 6-Apr-2019.)

Assertion

Ref	Expression
bj-1nel0	|- 1o e/ { (/) }

Proof of Theorem bj-1nel0

Step	Hyp	Ref	Expression
1		1n0 7575	. . . 4 |- 1o =/= (/)
2	1	neii 2796	. . 3 |- -. 1o = (/)
3		elsni 4194	. . 3 |- ( 1o e. { (/) } -> 1o = (/) )
4	2, 3	mto 188	. 2 |- -. 1o e. { (/) }
5	4	nelir 2900	1 |- 1o e/ { (/) }

Syntax hints:   = wceq 1483   e. wcel 1990   e/ wnel 2897   (/)c0 3915   {csn 4177   1oc1o 7553

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1722  ax-4 1737  ax-5 1839  ax-6 1888  ax-7 1935  ax-9 1999  ax-10 2019  ax-11 2034  ax-12 2047  ax-13 2246  ax-ext 2602  ax-nul 4789

This theorem depends on definitions:  df-bi 197  df-or 385  df-an 386  df-tru 1486  df-ex 1705  df-nf 1710  df-sb 1881  df-clab 2609  df-cleq 2615  df-clel 2618  df-nfc 2753  df-ne 2795  df-nel 2898  df-v 3202  df-dif 3577  df-un 3579  df-nul 3916  df-sn 4178  df-suc 5729  df-1o 7560

This theorem is referenced by: (None)