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Theorem nfbii 1775
Description: Equality theorem for the non-freeness predicate. (Contributed by Mario Carneiro, 11-Aug-2016.) df-nf 1707 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 1774 . 2 (∀𝑥(𝜑𝜓) → (Ⅎ𝑥𝜑 ↔ Ⅎ𝑥𝜓))
2 nfbii.1 . 2 (𝜑𝜓)
31, 2mpg 1721 1 (Ⅎ𝑥𝜑 ↔ Ⅎ𝑥𝜓)
Colors of variables: wff setvar class
Syntax hints:  wb 196  wnf 1705
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1719  ax-4 1734
This theorem depends on definitions:  df-bi 197  df-ex 1702  df-nf 1707
This theorem is referenced by:  nfxfr  1776  nfxfrd  1777  dvelimhw  2170  nfeqf1  2298  dfnfc2  4420  dfnfc2OLD  4421  bj-dvelimdv1  32477  bj-nfcf  32564  iunconnlem2  38651
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