Theorem sbf2 2028

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 1788	. 2 ⊢ Ⅎx∀xφ
2	1	sbf 2026	1 ⊢ ([y / x]∀xφ ↔ ∀xφ)

Syntax hints:   ↔ wb 176  ∀wal 1540  [wsb 1648

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1546  ax-5 1557  ax-17 1616  ax-9 1654  ax-8 1675  ax-6 1729  ax-7 1734  ax-11 1746  ax-12 1925

This theorem depends on definitions:  df-bi 177  df-an 360  df-tru 1319  df-ex 1542  df-nf 1545  df-sb 1649

This theorem is referenced by: (None)