Theorem 19.3h 1442

Description: A wff may be quantified with a variable not free in it. Theorem 19.3 of [Margaris] p. 89. (Contributed by NM, 5-Aug-1993.) (Revised by NM, 21-May-2007.)

Hypothesis

Ref	Expression
19.3h.1	⊢ (φ → ∀xφ)

Assertion

Ref	Expression
19.3h	⊢ (∀xφ ↔ φ)

Proof of Theorem 19.3h

Step	Hyp	Ref	Expression
1		ax-4 1397	. 2 ⊢ (∀xφ → φ)
2		19.3h.1	. 2 ⊢ (φ → ∀xφ)
3	1, 2	impbii 117	1 ⊢ (∀xφ ↔ φ)

Syntax hints:   → wi 4   ↔ wb 98  ∀wal 1240

This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia2 100  ax-ia3 101  ax-4 1397

This theorem depends on definitions:  df-bi 110

This theorem is referenced by:  19.27h  1449  19.28h  1451  equsalh  1611  2eu4  1990