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Theorem nfs1f 2520
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 2517 . 2 ([𝑦 / 𝑥]𝜑𝜑)
32, 1nfxfr 1928 1 𝑥[𝑦 / 𝑥]𝜑
Colors of variables: wff setvar class
Syntax hints:  wnf 1857  [wsb 2046
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1871  ax-4 1886  ax-5 1988  ax-6 2054  ax-7 2090  ax-12 2196  ax-13 2391
This theorem depends on definitions:  df-bi 197  df-an 385  df-ex 1854  df-nf 1859  df-sb 2047
This theorem is referenced by: (None)
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