Theorem nesym 2250

Description: Characterization of inequality in terms of reversed equality (see bicom 128). (Contributed by BJ, 7-Jul-2018.)

Assertion

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

Proof of Theorem nesym

Step	Hyp	Ref	Expression
1		eqcom 2042	. 2 |- ( A = B <-> B = A )
2	1	necon3abii 2241	1 |- ( A =/= B <-> -. B = A )

Syntax hints:   -. wn 3   <-> wb 98   = wceq 1243   =/= wne 2204

This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 99  ax-ia2 100  ax-ia3 101  ax-in1 544  ax-in2 545  ax-5 1336  ax-gen 1338  ax-ext 2022

This theorem depends on definitions:  df-bi 110  df-cleq 2033  df-ne 2206

This theorem is referenced by:  nesymi  2251  nesymir  2252  0neqopab  5550  fzdifsuc  8943