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Theorem nfnf1 1409
Description: x is not free in xφ. (Contributed by Mario Carneiro, 11-Aug-2016.)
Assertion
Ref Expression
nfnf1 xxφ

Proof of Theorem nfnf1
StepHypRef Expression
1 df-nf 1323 . 2 (Ⅎxφx(φxφ))
2 nfa1 1407 . 2 xx(φxφ)
31, 2nfxfr 1336 1 xxφ
Colors of variables: wff set class
Syntax hints:  wi 4  wal 1221  wnf 1322
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 1309  ax-gen 1311  ax-ial 1400
This theorem depends on definitions:  df-bi 110  df-nf 1323
This theorem is referenced by:  nfimd  1450  nfnt  1519  nfald  1616  equs5or  1684  sbcomxyyz  1819  nfsb4t  1863  nfnfc1  2154  sbcnestgf  2865  dfnfc2  3561  bdsepnft  8271  setindft  8345  strcollnft  8364
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