Theorem sbf2 1789

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 1552	. 2 ⊢ Ⅎ𝑥∀𝑥𝜑
2	1	sbf 1788	1 ⊢ ([𝑦 / 𝑥]∀𝑥𝜑 ↔ ∀𝑥𝜑)

Syntax hints:   ↔ wb 105  ∀wal 1362  [wsb 1773

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 106  ax-ia2 107  ax-ia3 108  ax-5 1458  ax-gen 1460  ax-ie1 1504  ax-ie2 1505  ax-4 1521  ax-i9 1541  ax-ial 1545

This theorem depends on definitions:  df-bi 117  df-nf 1472  df-sb 1774

This theorem is referenced by: (None)