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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
StepHypRef Expression
1 neii.1 . 2  |-  A  =/= 
B
2 df-ne 2250 . 2  |-  ( A  =/=  B  <->  -.  A  =  B )
31, 2mpbi 143 1  |-  -.  A  =  B
Colors of variables: wff set class
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
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