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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
StepHypRef Expression
1 neii.1 . 2  |-  A  =/= 
B
2 df-ne 2206 . 2  |-  ( A  =/=  B  <->  -.  A  =  B )
31, 2mpbi 133 1  |-  -.  A  =  B
Colors of variables: wff set class
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
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