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Theorem nfs1f 2382
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 . . 3 𝑥𝜑
21sbf 2379 . 2 ([𝑦 / 𝑥]𝜑𝜑)
32, 1nfxfr 1776 1 𝑥[𝑦 / 𝑥]𝜑
Colors of variables: wff setvar class
Syntax hints:  wnf 1705  [wsb 1877
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1719  ax-4 1734  ax-5 1836  ax-6 1885  ax-7 1932  ax-12 2044  ax-13 2245
This theorem depends on definitions:  df-bi 197  df-an 386  df-ex 1702  df-nf 1707  df-sb 1878
This theorem is referenced by: (None)
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