Theorem neii 2251

Description: Inference associated with df-ne 2250. (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 2250	. 2 |- ( A =/= B <-> -. A = B )
3	1, 2	mpbi 143	1 |- -. A = B

Syntax hints:   -. wn 3   = wceq 1285   =/= wne 2249

This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 104

This theorem depends on definitions:  df-bi 115  df-ne 2250

This theorem is referenced by:  2dom  6374  updjudhcoinrg  6575  ine0  7635  inelr  7821  xrltnr  9001  pnfnlt  9008  xrlttri3  9018  nltpnft  9030  3lcm2e6woprm  10693  6lcm4e12  10694