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Theorem nfnf1 1544
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 1461 . 2 (Ⅎ𝑥𝜑 ↔ ∀𝑥(𝜑 → ∀𝑥𝜑))
2 nfa1 1541 . 2 𝑥𝑥(𝜑 → ∀𝑥𝜑)
31, 2nfxfr 1474 1 𝑥𝑥𝜑
Colors of variables: wff set class
Syntax hints:  wi 4  wal 1351  wnf 1460
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 106  ax-ia2 107  ax-ia3 108  ax-5 1447  ax-gen 1449  ax-ial 1534
This theorem depends on definitions:  df-bi 117  df-nf 1461
This theorem is referenced by:  nfimd  1585  nfnt  1656  nfald  1760  equs5or  1830  sbcomxyyz  1972  nfsb4t  2014  nfnfc1  2322  nfabdw  2338  sbcnestgf  3110  dfnfc2  3829  bdsepnft  14678  setindft  14756  strcollnft  14775
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