Theorem bnj923 30838

Description: First-order logic and set theory. (Contributed by Jonathan Ben-Naim, 3-Jun-2011.) (New usage is discouraged.)

Hypothesis

Ref	Expression
bnj923.1	|- D = ( om \ { (/) } )

Assertion

Ref	Expression
bnj923	|- ( n e. D -> n e. om )

Proof of Theorem bnj923

Step	Hyp	Ref	Expression
1		eldifi 3732	. 2 |- ( n e. ( om \ { (/) } ) -> n e. om )
2		bnj923.1	. 2 |- D = ( om \ { (/) } )
3	1, 2	eleq2s 2719	1 |- ( n e. D -> n e. om )

Syntax hints:   -> wi 4   = wceq 1483   e. wcel 1990   \ cdif 3571   (/)c0 3915   {csn 4177   omcom 7065

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

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-v 3202  df-dif 3577

This theorem is referenced by:  bnj1098  30854  bnj544  30964  bnj546  30966  bnj594  30982  bnj580  30983  bnj966  31014  bnj967  31015  bnj970  31017  bnj1001  31028  bnj1053  31044  bnj1071  31045  bnj1118  31052  bnj1128  31058  bnj1145  31061