Theorem bj-n0i 32935

Description: Inference associated with n0 3931. Shortens 2ndcdisj 21259 (2888>2878), notzfaus 4840 (264>253). (Contributed by BJ, 22-Apr-2019.)

Hypothesis

Ref	Expression
bj-n0i.1	|- A =/= (/)

Assertion

Ref	Expression
bj-n0i	|- E. x x e. A

Distinct variable group:   x, A

Proof of Theorem bj-n0i

Step	Hyp	Ref	Expression
1		bj-n0i.1	. 2 |- A =/= (/)
2		n0 3931	. 2 |- ( A =/= (/) <-> E. x x e. A )
3	1, 2	mpbi 220	1 |- E. x x e. A

Syntax hints:   E.wex 1704   e. wcel 1990   =/= wne 2794   (/)c0 3915

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-ne 2795  df-v 3202  df-dif 3577  df-nul 3916

This theorem is referenced by: (None)