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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 𝐴𝐵
Assertion
Ref Expression
neii ¬ 𝐴 = 𝐵

Proof of Theorem neii
StepHypRef Expression
1 neii.1 . 2 𝐴𝐵
2 df-ne 2206 . 2 (𝐴𝐵 ↔ ¬ 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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