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Theorem nfcjust 2963
 Description: Justification theorem for df-nfc 2964. (Contributed by Mario Carneiro, 13-Oct-2016.)
Assertion
Ref Expression
nfcjust (∀𝑦𝑥 𝑦𝐴 ↔ ∀𝑧𝑥 𝑧𝐴)
Distinct variable groups:   𝑥,𝑦,𝑧   𝑦,𝐴,𝑧
Allowed substitution hint:   𝐴(𝑥)

Proof of Theorem nfcjust
StepHypRef Expression
1 eleq1w 2898 . . 3 (𝑦 = 𝑧 → (𝑦𝐴𝑧𝐴))
21nfbidv 1924 . 2 (𝑦 = 𝑧 → (Ⅎ𝑥 𝑦𝐴 ↔ Ⅎ𝑥 𝑧𝐴))
32cbvalvw 2044 1 (∀𝑦𝑥 𝑦𝐴 ↔ ∀𝑧𝑥 𝑧𝐴)
 Colors of variables: wff setvar class Syntax hints:   ↔ wb 209  ∀wal 1536  Ⅎwnf 1785   ∈ wcel 2115 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1797  ax-4 1811  ax-5 1912  ax-6 1971  ax-7 2016  ax-8 2117 This theorem depends on definitions:  df-bi 210  df-an 400  df-ex 1782  df-nf 1786  df-clel 2896 This theorem is referenced by: (None)
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