Theorem nesym 2447

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 2233	. 2 |- ( A = B <-> B = A )
2	1	necon3abii 2438	1 |- ( A =/= B <-> -. B = A )

Syntax hints:   -. wn 3   <-> wb 105   = wceq 1397   =/= wne 2402

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 619  ax-in2 620  ax-5 1495  ax-gen 1497  ax-ext 2213

This theorem depends on definitions:  df-bi 117  df-cleq 2224  df-ne 2403

This theorem is referenced by:  nesymi  2448  nesymir  2449  0neqopab  6065  fzdifsuc  10315  isprm3  12689