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Theorem nfnf1 1523
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 1437 . 2 (Ⅎ𝑥𝜑 ↔ ∀𝑥(𝜑 → ∀𝑥𝜑))
2 nfa1 1521 . 2 𝑥𝑥(𝜑 → ∀𝑥𝜑)
31, 2nfxfr 1450 1 𝑥𝑥𝜑
Colors of variables: wff set class
Syntax hints:  wi 4  wal 1329  wnf 1436
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 105  ax-ia2 106  ax-ia3 107  ax-5 1423  ax-gen 1425  ax-ial 1514
This theorem depends on definitions:  df-bi 116  df-nf 1437
This theorem is referenced by:  nfimd  1564  nfnt  1634  nfald  1733  equs5or  1802  sbcomxyyz  1945  nfsb4t  1989  nfnfc1  2284  sbcnestgf  3051  dfnfc2  3754  bdsepnft  13144  setindft  13222  strcollnft  13241
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