Theorem nne 1589

Description: Negation of inequality.

Assertion

Ref	Expression
nne	|- (-. A =/= B <-> A = B)

Proof of Theorem nne

Step	Hyp	Ref	Expression
1		df-ne 1587	. . 3 |- (A =/= B <-> -. A = B)
2	1	con2bii 221	. 2 |- (A = B <-> -. A =/= B)
3	2	bicomi 172	1 |- (-. A =/= B <-> A = B)

Syntax hints:  -. wn 2   <-> wb 146   = wceq 956   =/= wne 1585

This theorem is referenced by:  necon4bid 1630  fr0 2927  xpeq0 3467  1re 5435  elcls 7704  bcthlem7 8005  0ngrp 8055  nmlno0lem 8453  lnon0 8458  nmlnop0ALT 9920  atom1d 10280

This theorem was proved from axioms:  ax-1 4  ax-2 5  ax-3 6  ax-mp 7

This theorem depends on definitions:  df-bi 147  df-ne 1587

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