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Theorem neleq2 2608
 Description: Equality theorem for negated membership. (Contributed by NM, 20-Nov-1994.)
Assertion
Ref Expression
neleq2 (A = B → (C AC B))

Proof of Theorem neleq2
StepHypRef Expression
1 eleq2 2414 . . 3 (A = B → (C AC B))
21notbid 285 . 2 (A = B → (¬ C A ↔ ¬ C B))
3 df-nel 2519 . 2 (C A ↔ ¬ C A)
4 df-nel 2519 . 2 (C B ↔ ¬ C B)
52, 3, 43bitr4g 279 1 (A = B → (C AC B))
 Colors of variables: wff setvar class Syntax hints:  ¬ wn 3   → wi 4   ↔ wb 176   = wceq 1642   ∈ wcel 1710   ∉ wnel 2517 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1546  ax-5 1557  ax-17 1616  ax-9 1654  ax-8 1675  ax-11 1746  ax-ext 2334 This theorem depends on definitions:  df-bi 177  df-an 360  df-ex 1542  df-cleq 2346  df-clel 2349  df-nel 2519 This theorem is referenced by:  neleq12d  2609
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