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Theorem nfnbiOLD 1859
Description: Obsolete version of nfnbi 1858 as of 6-Oct-2024. (Contributed by BJ, 6-May-2019.) (Proof modification is discouraged.) (New usage is discouraged.)
Assertion
Ref Expression
nfnbiOLD (Ⅎ𝑥𝜑 ↔ Ⅎ𝑥 ¬ 𝜑)

Proof of Theorem nfnbiOLD
StepHypRef Expression
1 orcom 869 . 2 ((∀𝑥𝜑 ∨ ∀𝑥 ¬ 𝜑) ↔ (∀𝑥 ¬ 𝜑 ∨ ∀𝑥𝜑))
2 nf3 1789 . 2 (Ⅎ𝑥𝜑 ↔ (∀𝑥𝜑 ∨ ∀𝑥 ¬ 𝜑))
3 nf3 1789 . . 3 (Ⅎ𝑥 ¬ 𝜑 ↔ (∀𝑥 ¬ 𝜑 ∨ ∀𝑥 ¬ ¬ 𝜑))
4 notnotb 315 . . . . 5 (𝜑 ↔ ¬ ¬ 𝜑)
54albii 1822 . . . 4 (∀𝑥𝜑 ↔ ∀𝑥 ¬ ¬ 𝜑)
65orbi2i 912 . . 3 ((∀𝑥 ¬ 𝜑 ∨ ∀𝑥𝜑) ↔ (∀𝑥 ¬ 𝜑 ∨ ∀𝑥 ¬ ¬ 𝜑))
73, 6bitr4i 278 . 2 (Ⅎ𝑥 ¬ 𝜑 ↔ (∀𝑥 ¬ 𝜑 ∨ ∀𝑥𝜑))
81, 2, 73bitr4i 303 1 (Ⅎ𝑥𝜑 ↔ Ⅎ𝑥 ¬ 𝜑)
Colors of variables: wff setvar class
Syntax hints:  ¬ wn 3  wb 205  wo 846  wal 1540  wnf 1786
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1798  ax-4 1812
This theorem depends on definitions:  df-bi 206  df-or 847  df-ex 1783  df-nf 1787
This theorem is referenced by: (None)
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