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Theorem neeq2 2525
 Description: Equality theorem for inequality. (Contributed by NM, 19-Nov-1994.)
Assertion
Ref Expression
neeq2 (A = B → (CACB))

Proof of Theorem neeq2
StepHypRef Expression
1 eqeq2 2362 . . 3 (A = B → (C = AC = B))
21notbid 285 . 2 (A = B → (¬ C = A ↔ ¬ C = B))
3 df-ne 2518 . 2 (CA ↔ ¬ C = A)
4 df-ne 2518 . 2 (CB ↔ ¬ C = B)
52, 3, 43bitr4g 279 1 (A = B → (CACB))
 Colors of variables: wff setvar class Syntax hints:  ¬ wn 3   → wi 4   ↔ wb 176   = wceq 1642   ≠ wne 2516 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-ex 1542  df-cleq 2346  df-ne 2518 This theorem is referenced by:  neeq2i  2527  neeq2d  2530  psseq2  3357  nfunv  5138  enprmapc  6083  ce2  6192
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