Theorem nesym 2290

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 2083	. 2 |- ( A = B <-> B = A )
2	1	necon3abii 2281	1 |- ( A =/= B <-> -. B = A )

Syntax hints:   -. wn 3   <-> wb 103   = wceq 1284   =/= wne 2245

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 576  ax-in2 577  ax-5 1376  ax-gen 1378  ax-ext 2063

This theorem depends on definitions:  df-bi 115  df-cleq 2074  df-ne 2246

This theorem is referenced by:  nesymi  2291  nesymir  2292  0neqopab  5570  fzdifsuc  9098  isprm3  10500