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Theorem sbh 2380
Description: Substitution for a variable not free in a wff does not affect it. (Contributed by NM, 14-May-1993.)
Hypothesis
Ref Expression
sbh.1 (𝜑 → ∀𝑥𝜑)
Assertion
Ref Expression
sbh ([𝑦 / 𝑥]𝜑𝜑)

Proof of Theorem sbh
StepHypRef Expression
1 sbh.1 . . 3 (𝜑 → ∀𝑥𝜑)
21nf5i 2021 . 2 𝑥𝜑
32sbf 2379 1 ([𝑦 / 𝑥]𝜑𝜑)
Colors of variables: wff setvar class
Syntax hints:  wi 4  wb 196  wal 1478  [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-10 2016  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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