Theorem sbf2 2267

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

Step	Hyp	Ref	Expression
1		nfa1 2150	. 2 ⊢ Ⅎ𝑥∀𝑥𝜑
2	1	sbf 2266	1 ⊢ ([𝑦 / 𝑥]∀𝑥𝜑 ↔ ∀𝑥𝜑)

Syntax hints:   ↔ wb 205  ∀wal 1537  [wsb 2068

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1799  ax-4 1813  ax-5 1914  ax-6 1972  ax-7 2012  ax-10 2139  ax-12 2173

This theorem depends on definitions:  df-bi 206  df-or 844  df-ex 1784  df-nf 1788  df-sb 2069

This theorem is referenced by: (None)