Theorem nesym 2300

Description: Characterization of inequality in terms of reversed equality (see bicom 138). (Contributed by BJ, 7-Jul-2018.)

Assertion

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

Proof of Theorem nesym

Step	Hyp	Ref	Expression
1		eqcom 2090	. 2 |- ( A = B <-> B = A )
2	1	necon3abii 2291	1 |- ( A =/= B <-> -. B = A )

Syntax hints:   -. wn 3   <-> wb 103   = wceq 1289   =/= wne 2255

This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 104  ax-ia2 105  ax-ia3 106  ax-in1 579  ax-in2 580  ax-5 1381  ax-gen 1383  ax-ext 2070

This theorem depends on definitions:  df-bi 115  df-cleq 2081  df-ne 2256

This theorem is referenced by:  nesymi  2301  nesymir  2302  0neqopab  5694  fzdifsuc  9495  isprm3  11378