Theorem ax467to4 2170

Description: Re-derivation of ax-4 2135 from ax467 2169. Only propositional calculus is used by the re-derivation. (Contributed by NM, 19-Nov-2006.) (Proof modification is discouraged.) (New usage is discouraged.)

Assertion

Ref	Expression
ax467to4	⊢ (∀xφ → φ)

Proof of Theorem ax467to4

Step	Hyp	Ref	Expression
1		ax-1 6	. 2 ⊢ (∀xφ → (∀x∀x ¬ ∀x∀xφ → ∀xφ))
2		ax467 2169	. 2 ⊢ ((∀x∀x ¬ ∀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-gen 1546  ax-5 1557  ax-7 1734  ax-4 2135  ax-5o 2136  ax-6o 2137

This theorem is referenced by: (None)