Metamath Proof Explorer < Previous   Next > Nearby theorems Mirrors  >  Home  >  MPE Home  >  Th. List  >  nfcrii Unicode version

Theorem nfcrii 2412
 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 2411 . . . 4
31, 2ax-mp 8 . . 3
43nfri 1742 . 2
54hblem 2387 1
 Colors of variables: wff set class Syntax hints:   wi 4  wal 1527  wnf 1531   wcel 1684  wnfc 2406 This theorem is referenced by:  nfcri  2413  abeq2f  23129  rabid2f  23135  bnj1230  28835  bnj1000  28973  bnj1204  29042  bnj1307  29053  bnj1311  29054  bnj1398  29064  bnj1466  29083  bnj1467  29084  bnj1523  29101 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1533  ax-5 1544  ax-17 1603  ax-9 1635  ax-8 1643  ax-6 1703  ax-7 1708  ax-11 1715  ax-12 1866  ax-ext 2264 This theorem depends on definitions:  df-bi 177  df-or 359  df-an 360  df-tru 1310  df-ex 1529  df-nf 1532  df-sb 1630  df-cleq 2276  df-clel 2279  df-nfc 2408
 Copyright terms: Public domain W3C validator