Theorem nesym 2409

Description: Characterization of inequality in terms of reversed equality (see bicom 140). (Contributed by BJ, 7-Jul-2018.)

Assertion

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

Proof of Theorem nesym

Step	Hyp	Ref	Expression
1		eqcom 2195	. 2 |- ( A = B <-> B = A )
2	1	necon3abii 2400	1 |- ( A =/= B <-> -. B = A )

Syntax hints:   -. wn 3   <-> wb 105   = wceq 1364   =/= wne 2364

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 106  ax-ia2 107  ax-ia3 108  ax-in1 615  ax-in2 616  ax-5 1458  ax-gen 1460  ax-ext 2175

This theorem depends on definitions:  df-bi 117  df-cleq 2186  df-ne 2365

This theorem is referenced by:  nesymi  2410  nesymir  2411  0neqopab  5963  fzdifsuc  10147  isprm3  12256