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Theorem nfbii 1848
 Description: Equality theorem for the non-freeness predicate. (Contributed by Mario Carneiro, 11-Aug-2016.) df-nf 1781 changed. (Revised by Wolf Lammen, 12-Sep-2021.)
Hypothesis
Ref Expression
nfbii.1 (𝜑𝜓)
Assertion
Ref Expression
nfbii (Ⅎ𝑥𝜑 ↔ Ⅎ𝑥𝜓)

Proof of Theorem nfbii
StepHypRef Expression
1 nfbiit 1847 . 2 (∀𝑥(𝜑𝜓) → (Ⅎ𝑥𝜑 ↔ Ⅎ𝑥𝜓))
2 nfbii.1 . 2 (𝜑𝜓)
31, 2mpg 1794 1 (Ⅎ𝑥𝜑 ↔ Ⅎ𝑥𝜓)
 Colors of variables: wff setvar class Syntax hints:   ↔ wb 208  Ⅎwnf 1780 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1792  ax-4 1806 This theorem depends on definitions:  df-bi 209  df-ex 1777  df-nf 1781 This theorem is referenced by:  nfxfr  1849  nfxfrd  1850  dvelimhw  2362  nfeqf1  2393  nfceqi  2973  dfnfc2  4849  bj-dvelimdv1  34171  bj-nfcf  34237  iunconnlem2  41262
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