Theorem ax46to4 2163

Description: Re-derivation of ax-4 2135 from ax46 2162. Only propositional calculus is used for the re-derivation. (Contributed by Scott Fenton, 12-Sep-2005.) (Proof modification is discouraged.) (New usage is discouraged.)

Assertion

Ref	Expression
ax46to4	⊢ (∀xφ → φ)

Proof of Theorem ax46to4

Step	Hyp	Ref	Expression
1		ax-1 6	. 2 ⊢ (∀xφ → (∀x ¬ ∀xφ → ∀xφ))
2		ax46 2162	. 2 ⊢ ((∀x ¬ ∀xφ → ∀xφ) → φ)
3	1, 2	syl 15	1 ⊢ (∀xφ → φ)

Syntax hints:  ¬ wn 3   → wi 4  ∀wal 1540

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-4 2135  ax-6o 2137

This theorem is referenced by: (None)