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Theorem nfcrii 2168
 Description: Consequence of the not-free predicate. (Contributed by Mario Carneiro, 11-Aug-2016.)
Hypothesis
Ref Expression
nfcri.1 xA
Assertion
Ref Expression
nfcrii (y Ax y A)
Distinct variable group:   x,y
Allowed substitution hints:   A(x,y)

Proof of Theorem nfcrii
Dummy variable z is distinct from all other variables.
StepHypRef Expression
1 nfcri.1 . . . 4 xA
2 nfcr 2167 . . . 4 (xA → Ⅎx z A)
31, 2ax-mp 7 . . 3 x z A
43nfri 1409 . 2 (z Ax z A)
54hblem 2142 1 (y Ax y A)
 Colors of variables: wff set class Syntax hints:   → wi 4  ∀wal 1240  Ⅎwnf 1346   ∈ wcel 1390  Ⅎwnfc 2162 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-io 629  ax-5 1333  ax-7 1334  ax-gen 1335  ax-ie1 1379  ax-ie2 1380  ax-8 1392  ax-10 1393  ax-11 1394  ax-i12 1395  ax-bnd 1396  ax-4 1397  ax-17 1416  ax-i9 1420  ax-ial 1424  ax-i5r 1425  ax-ext 2019 This theorem depends on definitions:  df-bi 110  df-nf 1347  df-sb 1643  df-cleq 2030  df-clel 2033  df-nfc 2164 This theorem is referenced by:  nfcri  2169
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