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Theorem dvelimc 2510
 Description: Version of dvelim 2016 for classes. (Contributed by Mario Carneiro, 8-Oct-2016.)
Hypotheses
Ref Expression
dvelimc.1 xA
dvelimc.2 zB
dvelimc.3 (z = yA = B)
Assertion
Ref Expression
dvelimc x x = yxB)

Proof of Theorem dvelimc
StepHypRef Expression
1 nftru 1554 . . 3 x
2 nftru 1554 . . 3 z
3 dvelimc.1 . . . 4 xA
43a1i 10 . . 3 ( ⊤ → xA)
5 dvelimc.2 . . . 4 zB
65a1i 10 . . 3 ( ⊤ → zB)
7 dvelimc.3 . . . 4 (z = yA = B)
87a1i 10 . . 3 ( ⊤ → (z = yA = B))
91, 2, 4, 6, 8dvelimdc 2509 . 2 ( ⊤ → (¬ x x = yxB))
109trud 1323 1 x x = yxB)
 Colors of variables: wff setvar class Syntax hints:  ¬ wn 3   → wi 4   ⊤ wtru 1316  ∀wal 1540   = wceq 1642  Ⅎwnfc 2476 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-6 1729  ax-7 1734  ax-11 1746  ax-12 1925  ax-ext 2334 This theorem depends on definitions:  df-bi 177  df-an 360  df-tru 1319  df-ex 1542  df-nf 1545  df-sb 1649  df-cleq 2346  df-clel 2349  df-nfc 2478 This theorem is referenced by:  nfcvf  2511
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