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Theorem nfs1f 1710
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 1457 . . 3 (𝜑 → ∀𝑥𝜑)
32sbh 1706 . 2 ([𝑦 / 𝑥]𝜑𝜑)
43, 1nfxfr 1408 1 𝑥[𝑦 / 𝑥]𝜑
Colors of variables: wff set class
Syntax hints:  wnf 1394  [wsb 1692
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-ie1 1427  ax-ie2 1428  ax-4 1445  ax-i9 1468  ax-ial 1472
This theorem depends on definitions:  df-bi 115  df-nf 1395  df-sb 1693
This theorem is referenced by: (None)
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