Theorem sbf2 1661

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 1434	. 2 ⊢ Ⅎ𝑥∀𝑥𝜑
2	1	sbf 1660	1 ⊢ ([𝑦 / 𝑥]∀𝑥𝜑 ↔ ∀𝑥𝜑)

Syntax hints:   ↔ wb 98  ∀wal 1241  [wsb 1645

This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 99  ax-ia2 100  ax-ia3 101  ax-5 1336  ax-gen 1338  ax-ie1 1382  ax-ie2 1383  ax-4 1400  ax-i9 1423  ax-ial 1427

This theorem depends on definitions:  df-bi 110  df-nf 1350  df-sb 1646

This theorem is referenced by: (None)