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Theorem nfbii2 33938
Description: Equality deduction for not-freeness. (Contributed by Giovanni Mascellani, 10-Apr-2018.)
Assertion
Ref Expression
nfbii2 (∀𝑥(𝜑𝜓) → (Ⅎ𝑥𝜑 ↔ Ⅎ𝑥𝜓))

Proof of Theorem nfbii2
StepHypRef Expression
1 nfa1 2026 . 2 𝑥𝑥(𝜑𝜓)
2 sp 2051 . 2 (∀𝑥(𝜑𝜓) → (𝜑𝜓))
31, 2nfbidf 2090 1 (∀𝑥(𝜑𝜓) → (Ⅎ𝑥𝜑 ↔ Ⅎ𝑥𝜓))
Colors of variables: wff setvar class
Syntax hints:  wi 4  wb 196  wal 1479  wnf 1706
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1720  ax-4 1735  ax-5 1837  ax-6 1886  ax-7 1933  ax-10 2017  ax-12 2045
This theorem depends on definitions:  df-bi 197  df-or 385  df-ex 1703  df-nf 1708
This theorem is referenced by: (None)
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