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Theorem nfnf1 1481
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 1395 . 2 (Ⅎ𝑥𝜑 ↔ ∀𝑥(𝜑 → ∀𝑥𝜑))
2 nfa1 1479 . 2 𝑥𝑥(𝜑 → ∀𝑥𝜑)
31, 2nfxfr 1408 1 𝑥𝑥𝜑
Colors of variables: wff set class
Syntax hints:  wi 4  wal 1287  wnf 1394
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 104  ax-ia2 105  ax-ia3 106  ax-5 1381  ax-gen 1383  ax-ial 1472
This theorem depends on definitions:  df-bi 115  df-nf 1395
This theorem is referenced by:  nfimd  1522  nfnt  1591  nfald  1690  equs5or  1758  sbcomxyyz  1894  nfsb4t  1938  nfnfc1  2231  sbcnestgf  2977  dfnfc2  3666  bdsepnft  11435  setindft  11517  strcollnft  11536
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