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Theorem dvelimc 2923
Description: Version of dvelim 2442 for classes. Usage of this theorem is discouraged because it depends on ax-13 2363. (Contributed by Mario Carneiro, 8-Oct-2016.) (New usage is discouraged.)
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 1798 . . 3 𝑥
2 nftru 1798 . . 3 𝑧
3 dvelimc.1 . . . 4 𝑥𝐴
43a1i 11 . . 3 (⊤ → 𝑥𝐴)
5 dvelimc.2 . . . 4 𝑧𝐵
65a1i 11 . . 3 (⊤ → 𝑧𝐵)
7 dvelimc.3 . . . 4 (𝑧 = 𝑦𝐴 = 𝐵)
87a1i 11 . . 3 (⊤ → (𝑧 = 𝑦𝐴 = 𝐵))
91, 2, 4, 6, 8dvelimdc 2922 . 2 (⊤ → (¬ ∀𝑥 𝑥 = 𝑦𝑥𝐵))
109mptru 1540 1 (¬ ∀𝑥 𝑥 = 𝑦𝑥𝐵)
Colors of variables: wff setvar class
Syntax hints:  ¬ wn 3  wi 4  wal 1531   = wceq 1533  wtru 1534  wnfc 2875
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1789  ax-4 1803  ax-5 1905  ax-6 1963  ax-7 2003  ax-8 2100  ax-9 2108  ax-10 2129  ax-11 2146  ax-12 2163  ax-13 2363  ax-ext 2695
This theorem depends on definitions:  df-bi 206  df-an 396  df-or 845  df-tru 1536  df-ex 1774  df-nf 1778  df-cleq 2716  df-clel 2802  df-nfc 2877
This theorem is referenced by: (None)
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