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Theorem nfnf1 1452
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 1366 . 2 (Ⅎ𝑥𝜑 ↔ ∀𝑥(𝜑 → ∀𝑥𝜑))
2 nfa1 1450 . 2 𝑥𝑥(𝜑 → ∀𝑥𝜑)
31, 2nfxfr 1379 1 𝑥𝑥𝜑
Colors of variables: wff set class
Syntax hints:  wi 4  wal 1257  wnf 1365
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 103  ax-ia2 104  ax-ia3 105  ax-5 1352  ax-gen 1354  ax-ial 1443
This theorem depends on definitions:  df-bi 114  df-nf 1366
This theorem is referenced by:  nfimd  1493  nfnt  1562  nfald  1659  equs5or  1727  sbcomxyyz  1862  nfsb4t  1906  nfnfc1  2197  sbcnestgf  2925  dfnfc2  3626  bdsepnft  10394  setindft  10477  strcollnft  10496
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