Theorem neneq 2389

Description: From inequality to non-equality. (Contributed by Glauco Siliprandi, 11-Dec-2019.)

Assertion

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

Proof of Theorem neneq

Step	Hyp	Ref	Expression
1		id 19	. 2 |- ( A =/= B -> A =/= B )
2	1	neneqd 2388	1 |- ( A =/= B -> -. A = B )

Syntax hints:   -. wn 3   -> wi 4   = wceq 1364   =/= wne 2367

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 106

This theorem depends on definitions:  df-bi 117  df-ne 2368

This theorem is referenced by:  mpodifsnif  6015  gcd2n0cl  12136  isnsgrp  13049  lgsabs1  15280