Users' Mathboxes Mathbox for BJ < Previous   Next >
Nearby theorems
Mirrors  >  Home  >  MPE Home  >  Th. List  >   Mathboxes  >  bj-nnfe1 Structured version   Visualization version   GIF version

Theorem bj-nnfe1 34111
Description: See nfe1 2155. (Contributed by BJ, 12-Aug-2023.) (Proof modification is discouraged.)
Assertion
Ref Expression
bj-nnfe1 Ⅎ'𝑥𝑥𝜑

Proof of Theorem bj-nnfe1
StepHypRef Expression
1 bj-modal4e 34069 . 2 (∃𝑥𝑥𝜑 → ∃𝑥𝜑)
2 hbe1 2148 . 2 (∃𝑥𝜑 → ∀𝑥𝑥𝜑)
3 df-bj-nnf 34078 . 2 (Ⅎ'𝑥𝑥𝜑 ↔ ((∃𝑥𝑥𝜑 → ∃𝑥𝜑) ∧ (∃𝑥𝜑 → ∀𝑥𝑥𝜑)))
41, 2, 3mpbir2an 710 1 Ⅎ'𝑥𝑥𝜑
Colors of variables: wff setvar class
Syntax hints:  wi 4  wal 1536  wex 1781  Ⅎ'wnnf 34077
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1797  ax-4 1811  ax-5 1912  ax-6 1971  ax-7 2016  ax-10 2146  ax-12 2179
This theorem depends on definitions:  df-bi 210  df-an 400  df-ex 1782  df-bj-nnf 34078
This theorem is referenced by: (None)
  Copyright terms: Public domain W3C validator