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Theorem nfcrii 2571
 Description: Consequence of the not-free predicate. (Contributed by Mario Carneiro, 11-Aug-2016.)
Hypothesis
Ref Expression
nfcri.1
Assertion
Ref Expression
nfcrii
Distinct variable group:   ,
Allowed substitution hints:   (,)

Proof of Theorem nfcrii
Dummy variable is distinct from all other variables.
StepHypRef Expression
1 nfcri.1 . . . 4
2 nfcr 2570 . . . 4
31, 2ax-mp 5 . . 3
43nfri 1780 . 2
54hblem 2546 1
 Colors of variables: wff set class Syntax hints:   wi 4  wal 1550  wnf 1554   wcel 1727  wnfc 2565 This theorem is referenced by:  nfcri  2572  abeq2f  23991  bnj1230  29272  bnj1000  29410  bnj1204  29479  bnj1307  29490  bnj1311  29491  bnj1398  29501  bnj1466  29520  bnj1467  29521  bnj1523  29538 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1556  ax-5 1567  ax-17 1627  ax-9 1668  ax-8 1689  ax-6 1746  ax-7 1751  ax-11 1763  ax-12 1953  ax-ext 2423 This theorem depends on definitions:  df-bi 179  df-or 361  df-an 362  df-tru 1329  df-ex 1552  df-nf 1555  df-sb 1660  df-cleq 2435  df-clel 2438  df-nfc 2567
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