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Theorem ab0orvALT 4340
Description: Alternate proof of ab0orv 4339, 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 1918 . 2 𝑥𝜑
2 dfnf5 4338 . 2 (Ⅎ𝑥𝜑 ↔ ({𝑥𝜑} = V ∨ {𝑥𝜑} = ∅))
31, 2mpbi 229 1 ({𝑥𝜑} = V ∨ {𝑥𝜑} = ∅)
Colors of variables: wff setvar class
Syntax hints:  wo 846   = wceq 1542  wnf 1786  {cab 2710  Vcvv 3444  c0 4283
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1798  ax-4 1812  ax-5 1914  ax-6 1972  ax-7 2012  ax-9 2117  ax-10 2138  ax-11 2155  ax-12 2172  ax-ext 2704
This theorem depends on definitions:  df-bi 206  df-an 398  df-or 847  df-tru 1545  df-fal 1555  df-ex 1783  df-nf 1787  df-sb 2069  df-clab 2711  df-cleq 2725  df-v 3446  df-dif 3914  df-nul 4284
This theorem is referenced by: (None)
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