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Theorem nfs1f 1641
Description: If x is not free in φ, it is not free in [y / x]φ. (Contributed by Mario Carneiro, 11-Aug-2016.)
Hypothesis
Ref Expression
nfs1f.1 xφ
Assertion
Ref Expression
nfs1f x[y / x]φ

Proof of Theorem nfs1f
StepHypRef Expression
1 nfs1f.1 . . . 4 xφ
21nfri 1389 . . 3 (φxφ)
32sbh 1637 . 2 ([y / x]φφ)
43, 1nfxfr 1339 1 x[y / x]φ
Colors of variables: wff set class
Syntax hints:  wnf 1325  [wsb 1623
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 1312  ax-gen 1314  ax-ie1 1359  ax-ie2 1360  ax-4 1377  ax-i9 1400  ax-ial 1405
This theorem depends on definitions:  df-bi 110  df-nf 1326  df-sb 1624
This theorem is referenced by: (None)
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