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Theorem nfbii 1858
Description: Equality theorem for the nonfreeness predicate. (Contributed by Mario Carneiro, 11-Aug-2016.) df-nf 1791 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 1857 . 2 (∀𝑥(𝜑𝜓) → (Ⅎ𝑥𝜑 ↔ Ⅎ𝑥𝜓))
2 nfbii.1 . 2 (𝜑𝜓)
31, 2mpg 1804 1 (Ⅎ𝑥𝜑 ↔ Ⅎ𝑥𝜓)
Colors of variables: wff setvar class
Syntax hints:  wb 209  wnf 1790
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1802  ax-4 1816
This theorem depends on definitions:  df-bi 210  df-ex 1787  df-nf 1791
This theorem is referenced by:  nfxfr  1859  nfxfrd  1860  dvelimhw  2349  nfeqf1  2380  nfceqi  2897  nfra2w  3141  dfnfc2  4830  bj-dvelimdv1  34692  bj-nfcf  34768  iunconnlem2  42134
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