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Theorem nfcrii 2482
 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 2481 . . . 4 (xA → Ⅎx z A)
31, 2ax-mp 5 . . 3 x z A
43nfri 1762 . 2 (z Ax z A)
54hblem 2457 1 (y Ax y A)
 Colors of variables: wff setvar class Syntax hints:   → wi 4  ∀wal 1540  Ⅎwnf 1544   ∈ wcel 1710  Ⅎwnfc 2476 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-or 359  df-an 360  df-tru 1319  df-ex 1542  df-nf 1545  df-sb 1649  df-cleq 2346  df-clel 2349  df-nfc 2478 This theorem is referenced by:  nfcri  2483
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