Theorem ax46to4 1022

Description: Re-derivation of ax-4 977 from ax46 1021. Only propositional calculus is used for the re-derivation. (Contributed by Scott Fenton, 12-Sep-2005.)

Assertion

Ref	Expression
ax46to4	⊢ (∀xφ → φ)

Proof of Theorem ax46to4

Step	Hyp	Ref	Expression
1		ax-1 4	. 2 ⊢ (∀xφ → (∀x ¬ ∀xφ → ∀xφ))
2		ax46 1021	. 2 ⊢ ((∀x ¬ ∀xφ → ∀xφ) → φ)
3	1, 2	syl 10	1 ⊢ (∀xφ → φ)

Syntax hints:  ¬ wn 2   → wi 3  ∀wal 958

This theorem was proved from axioms:  ax-1 4  ax-2 5  ax-3 6  ax-mp 7  ax-4 977  ax-6o 982

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