Theorem neqne 2264

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

Assertion

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

Proof of Theorem neqne

Step	Hyp	Ref	Expression
1		id 19	. 2 |- ( -. A = B -> -. A = B )
2	1	neqned 2263	1 |- ( -. A = B -> A =/= B )

Syntax hints:   -. wn 3   -> wi 4   = wceq 1290   =/= wne 2256

This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 105  ax-ia2 106  ax-ia3 107

This theorem depends on definitions:  df-bi 116  df-ne 2257

This theorem is referenced by:  seq3f1olemstep  9993  dvdsabseq  11189