Theorem neii 2208

Description: Inference associated with df-ne 2206. (Contributed by BJ, 7-Jul-2018.)

Hypothesis

Ref	Expression
neii.1	|- A =/= B

Assertion

Ref	Expression
neii	|- -. A = B

Proof of Theorem neii

Step	Hyp	Ref	Expression
1		neii.1	. 2 |- A =/= B
2		df-ne 2206	. 2 |- ( A =/= B <-> -. A = B )
3	1, 2	mpbi 133	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

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

This theorem is referenced by:  2dom  6285  ine0  7391  inelr  7575  xrltnr  8701  pnfnlt  8708  xrlttri3  8718  nltpnft  8730