Theorem neir 2797

Description: Inference associated with df-ne 2795. (Contributed by BJ, 7-Jul-2018.)

Hypothesis

Ref	Expression
neir.1	|- -. A = B

Assertion

Ref	Expression
neir	|- A =/= B

Proof of Theorem neir

Step	Hyp	Ref	Expression
1		neir.1	. 2 |- -. A = B
2		df-ne 2795	. 2 |- ( A =/= B <-> -. A = B )
3	1, 2	mpbir 221	1 |- A =/= B

Syntax hints:   -. wn 3   = wceq 1483   =/= wne 2794

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8

This theorem depends on definitions:  df-bi 197  df-ne 2795

This theorem is referenced by:  nesymir  2852  nsuceq0  5805  ax1ne0  9981  ine0  10465  nnunb  11288  nosgnn0i  31812  bj-pinftynminfty  33114