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Theorem nfcjust 2163
 Description: Justification theorem for df-nfc 2164. (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 1418 . . 3 x y = z
2 eleq1 2097 . . 3 (y = z → (y Az A))
31, 2nfbidf 1429 . 2 (y = z → (Ⅎx y A ↔ Ⅎx z A))
43cbvalv 1791 1 (yx y Azx z A)
 Colors of variables: wff set class Syntax hints:   ↔ wb 98  ∀wal 1240  Ⅎwnf 1346   ∈ wcel 1390 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 99  ax-ia2 100  ax-ia3 101  ax-5 1333  ax-7 1334  ax-gen 1335  ax-ie1 1379  ax-ie2 1380  ax-8 1392  ax-4 1397  ax-17 1416  ax-i9 1420  ax-ial 1424  ax-ext 2019 This theorem depends on definitions:  df-bi 110  df-nf 1347  df-cleq 2030  df-clel 2033 This theorem is referenced by: (None)
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