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Theorem ab0orvALT 4374
Description: Alternate proof of ab0orv 4373, shorter but using more axioms. (Contributed by Mario Carneiro, 29-Aug-2013.) (Revised by BJ, 22-Mar-2020.) (Proof modification is discouraged.) (New usage is discouraged.)
Assertion
Ref Expression
ab0orvALT ({𝑥𝜑} = V ∨ {𝑥𝜑} = ∅)
Distinct variable group:   𝜑,𝑥

Proof of Theorem ab0orvALT
StepHypRef Expression
1 nfv 1909 . 2 𝑥𝜑
2 dfnf5 4372 . 2 (Ⅎ𝑥𝜑 ↔ ({𝑥𝜑} = V ∨ {𝑥𝜑} = ∅))
31, 2mpbi 229 1 ({𝑥𝜑} = V ∨ {𝑥𝜑} = ∅)
Colors of variables: wff setvar class
Syntax hints:  wo 844   = wceq 1533  wnf 1777  {cab 2703  Vcvv 3468  c0 4317
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-9 2108  ax-10 2129  ax-11 2146  ax-12 2163  ax-ext 2697
This theorem depends on definitions:  df-bi 206  df-an 396  df-or 845  df-tru 1536  df-fal 1546  df-ex 1774  df-nf 1778  df-sb 2060  df-clab 2704  df-cleq 2718  df-v 3470  df-dif 3946  df-nul 4318
This theorem is referenced by: (None)
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