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Theorem neneqd 2532
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 2518 . 2 (AB ↔ ¬ A = B)
31, 2sylib 188 1 (φ → ¬ A = B)
Colors of variables: wff setvar class
Syntax hints:  ¬ wn 3  wi 4   = wceq 1642  wne 2516
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8
This theorem depends on definitions:  df-bi 177  df-ne 2518
This theorem is referenced by:  necon2bi  2562  necon2i  2563  pm2.21ddne  2590  nulnnn  4556  enprmaplem3  6078
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