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Theorem nfbiiOLD 1824
 Description: Obsolete proof of nfbii 1770 as of 6-Oct-2021. (Contributed by Mario Carneiro, 11-Aug-2016.) (Proof modification is discouraged.) (New usage is discouraged.)
Hypothesis
Ref Expression
nfbiiOLD.1 (𝜑𝜓)
Assertion
Ref Expression
nfbiiOLD (Ⅎ𝑥𝜑 ↔ Ⅎ𝑥𝜓)

Proof of Theorem nfbiiOLD
StepHypRef Expression
1 nfbiiOLD.1 . . . 4 (𝜑𝜓)
21albii 1737 . . . 4 (∀𝑥𝜑 ↔ ∀𝑥𝜓)
31, 2imbi12i 339 . . 3 ((𝜑 → ∀𝑥𝜑) ↔ (𝜓 → ∀𝑥𝜓))
43albii 1737 . 2 (∀𝑥(𝜑 → ∀𝑥𝜑) ↔ ∀𝑥(𝜓 → ∀𝑥𝜓))
5 df-nfOLD 1712 . 2 (Ⅎ𝑥𝜑 ↔ ∀𝑥(𝜑 → ∀𝑥𝜑))
6 df-nfOLD 1712 . 2 (Ⅎ𝑥𝜓 ↔ ∀𝑥(𝜓 → ∀𝑥𝜓))
74, 5, 63bitr4i 291 1 (Ⅎ𝑥𝜑 ↔ Ⅎ𝑥𝜓)
 Colors of variables: wff setvar class Syntax hints:   → wi 4   ↔ wb 195  ∀wal 1473  ℲwnfOLD 1700 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1713  ax-4 1728 This theorem depends on definitions:  df-bi 196  df-nfOLD 1712 This theorem is referenced by:  nfxfrOLD  1825  nfxfrdOLD  1826
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