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Theorem sbf2 2386
Description: Substitution has no effect on a bound variable. (Contributed by NM, 1-Jul-2005.)
Assertion
Ref Expression
sbf2 ([𝑦 / 𝑥]∀𝑥𝜑 ↔ ∀𝑥𝜑)

Proof of Theorem sbf2
StepHypRef Expression
1 nfa1 2030 . 2 𝑥𝑥𝜑
21sbf 2384 1 ([𝑦 / 𝑥]∀𝑥𝜑 ↔ ∀𝑥𝜑)
Colors of variables: wff setvar class
Syntax hints:  wb 196  wal 1478  [wsb 1882
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 1841  ax-6 1890  ax-7 1937  ax-10 2021  ax-12 2049  ax-13 2250
This theorem depends on definitions:  df-bi 197  df-or 385  df-an 386  df-ex 1702  df-nf 1707  df-sb 1883
This theorem is referenced by: (None)
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