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Theorem neneq 2305
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
StepHypRef Expression
1 id 19 . 2  |-  ( A  =/=  B  ->  A  =/=  B )
21neneqd 2304 1  |-  ( A  =/=  B  ->  -.  A  =  B )
Colors of variables: wff set class
Syntax hints:   -. wn 3    -> wi 4    = wceq 1314    =/= wne 2283
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 105
This theorem depends on definitions:  df-bi 116  df-ne 2284
This theorem is referenced by:  mpodifsnif  5830  gcd2n0cl  11565
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