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Theorem nfcjust 2477
 Description: Justification theorem for df-nfc 2478. (Contributed by Mario Carneiro, 13-Oct-2016.)
Assertion
Ref Expression
nfcjust (yx y Azx z A)
Distinct variable groups:   x,y,z   y,A,z
Allowed substitution hint:   A(x)

Proof of Theorem nfcjust
StepHypRef Expression
1 nfv 1619 . . 3 x y = z
2 eleq1 2413 . . 3 (y = z → (y Az A))
31, 2nfbidf 1774 . 2 (y = z → (Ⅎx y A ↔ Ⅎx z A))
43cbvalv 2002 1 (yx y Azx z A)
 Colors of variables: wff setvar class Syntax hints:   ↔ wb 176  ∀wal 1540  Ⅎwnf 1544   = wceq 1642   ∈ wcel 1710 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1546  ax-5 1557  ax-17 1616  ax-9 1654  ax-8 1675  ax-6 1729  ax-7 1734  ax-11 1746  ax-12 1925  ax-ext 2334 This theorem depends on definitions:  df-bi 177  df-an 360  df-tru 1319  df-ex 1542  df-nf 1545  df-cleq 2346  df-clel 2349 This theorem is referenced by: (None)
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