Theorem neir 2311

Description: Inference associated with df-ne 2309. (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 2309	. 2 |- ( A =/= B <-> -. A = B )
3	1, 2	mpbir 145	1 |- A =/= B

Syntax hints:   -. wn 3   = wceq 1331   =/= wne 2308

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

This theorem depends on definitions:  df-bi 116  df-ne 2309

This theorem is referenced by:  exmidonfinlem  7049  ine0  8156  pwle2  13193