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Theorem nfcjust 2959
Description: Justification theorem for df-nfc 2960. (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 2892 . . 3 (𝑦 = 𝑧 → (𝑦𝐴𝑧𝐴))
21nfbidv 1914 . 2 (𝑦 = 𝑧 → (Ⅎ𝑥 𝑦𝐴 ↔ Ⅎ𝑥 𝑧𝐴))
32cbvalvw 2034 1 (∀𝑦𝑥 𝑦𝐴 ↔ ∀𝑧𝑥 𝑧𝐴)
Colors of variables: wff setvar class
Syntax hints:  wb 207  wal 1526  wnf 1775  wcel 2105
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1787  ax-4 1801  ax-5 1902  ax-6 1961  ax-7 2006  ax-8 2107
This theorem depends on definitions:  df-bi 208  df-an 397  df-ex 1772  df-nf 1776  df-clel 2890
This theorem is referenced by: (None)
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