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Theorem nfbii 1854
Description: Equality theorem for the nonfreeness predicate. (Contributed by Mario Carneiro, 11-Aug-2016.) df-nf 1787 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 1853 . 2 (∀𝑥(𝜑𝜓) → (Ⅎ𝑥𝜑 ↔ Ⅎ𝑥𝜓))
2 nfbii.1 . 2 (𝜑𝜓)
31, 2mpg 1800 1 (Ⅎ𝑥𝜑 ↔ Ⅎ𝑥𝜓)
Colors of variables: wff setvar class
Syntax hints:  wb 205  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-ex 1783  df-nf 1787
This theorem is referenced by:  nfxfr  1855  nfxfrd  1856  dvelimhw  2343  nfeqf1  2379  nfceqi  2904  nfra2wOLD  3155  dfnfc2  4863  bj-dvelimdv1  35036  bj-nfcf  35111  iunconnlem2  42555
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