Theorem neqne 2422

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 2421	1 |- ( -. A = B -> A =/= B )

Syntax hints:   -. wn 3   -> wi 4   = wceq 1398   =/= wne 2414

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 106  ax-ia2 107  ax-ia3 108

This theorem depends on definitions:  df-bi 117  df-ne 2415

This theorem is referenced by:  prfidceq  7201  xaddf  10196  seq3f1olemstep  10900  dvdsabseq  12558  lgsval  16003  upgriswlkdc  16481  umgrclwwlkge2  16523