Theorem neir 2209

Description: Inference associated with df-ne 2206. (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 2206	. 2 |- ( A =/= B <-> -. A = B )
3	1, 2	mpbir 134	1 |- A =/= B

Syntax hints:   -. wn 3   = wceq 1243   =/= wne 2204

This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 99  ax-ia2 100  ax-ia3 101

This theorem depends on definitions:  df-bi 110  df-ne 2206

This theorem is referenced by:  ine0  7391