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Theorem neir 2249
Description: Inference associated with df-ne 2247. (Contributed by BJ, 7-Jul-2018.)
Hypothesis
Ref Expression
neir.1  |-  -.  A  =  B
Assertion
Ref Expression
neir  |-  A  =/= 
B

Proof of Theorem neir
StepHypRef Expression
1 neir.1 . 2  |-  -.  A  =  B
2 df-ne 2247 . 2  |-  ( A  =/=  B  <->  -.  A  =  B )
31, 2mpbir 144 1  |-  A  =/= 
B
Colors of variables: wff set class
Syntax hints:   -. wn 3    = wceq 1285    =/= wne 2246
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 104  ax-ia2 105  ax-ia3 106
This theorem depends on definitions:  df-bi 115  df-ne 2247
This theorem is referenced by:  ine0  7565
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