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Theorem bj-nnfa1 36144
Description: See nfa1 2140. (Contributed by BJ, 12-Aug-2023.) (Proof modification is discouraged.)
Assertion
Ref Expression
bj-nnfa1 Ⅎ'𝑥𝑥𝜑

Proof of Theorem bj-nnfa1
StepHypRef Expression
1 hbe1a 2132 . 2 (∃𝑥𝑥𝜑 → ∀𝑥𝜑)
2 bj-modal4 36099 . 2 (∀𝑥𝜑 → ∀𝑥𝑥𝜑)
3 df-bj-nnf 36109 . 2 (Ⅎ'𝑥𝑥𝜑 ↔ ((∃𝑥𝑥𝜑 → ∀𝑥𝜑) ∧ (∀𝑥𝜑 → ∀𝑥𝑥𝜑)))
41, 2, 3mpbir2an 708 1 Ⅎ'𝑥𝑥𝜑
Colors of variables: wff setvar class
Syntax hints:  wi 4  wal 1531  wex 1773  Ⅎ'wnnf 36108
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-10 2129  ax-12 2163
This theorem depends on definitions:  df-bi 206  df-an 396  df-ex 1774  df-bj-nnf 36109
This theorem is referenced by: (None)
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