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Theorem neir 2206
Description: Inference associated with df-ne 2203. (Contributed by BJ, 7-Jul-2018.)
Hypothesis
Ref Expression
neir.1 ¬ A = B
Assertion
Ref Expression
neir AB

Proof of Theorem neir
StepHypRef Expression
1 neir.1 . 2 ¬ A = B
2 df-ne 2203 . 2 (AB ↔ ¬ A = B)
31, 2mpbir 134 1 AB
Colors of variables: wff set class
Syntax hints:  ¬ wn 3   = wceq 1242  wne 2201
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 99  ax-ia2 100  ax-ia3 101
This theorem depends on definitions:  df-bi 110  df-ne 2203
This theorem is referenced by:  ine0  7147
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