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Theorem neneqd 2205
Description: Deduction eliminating inequality definition. (Contributed by Jonathan Ben-Naim, 3-Jun-2011.)
Hypothesis
Ref Expression
neneqd.1 (φAB)
Assertion
Ref Expression
neneqd (φ → ¬ A = B)

Proof of Theorem neneqd
StepHypRef Expression
1 neneqd.1 . 2 (φAB)
2 df-ne 2188 . 2 (AB ↔ ¬ A = B)
31, 2sylib 127 1 (φ → ¬ A = B)
Colors of variables: wff set class
Syntax hints:  ¬ wn 3  wi 4   = wceq 1228  wne 2186
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 2188
This theorem is referenced by:  necon2bi  2238  necon2i  2239  pm2.21ddne  2266  nelrdva  2723  neq0r  3212  0inp0  3893  nndceq0  4266  frecsuclem3  5906  nnsucsssuc  5986  nqnq0pi  6293  ltxrlt  6686
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