Theorem a6e 688

Description: Abbreviated version of ax-6 675.

Assertion

Ref	Expression
a6e	⊢ (∃x∀xφ → φ)

Proof of Theorem a6e

Step	Hyp	Ref	Expression
1		df-ex 679	. 2 ⊢ (∃x∀xφ ↔ ¬ ∀x ¬ ∀xφ)
2		ax-6 675	. 2 ⊢ (¬ ∀x ¬ ∀xφ → φ)
3	1, 2	sylbi 174	1 ⊢ (∃x∀xφ → φ)

Syntax hints:  ¬ wn 1   → wi 2  ∀wal 672  ∃wex 678

This theorem is referenced by:  ax9 807

This theorem was proved from axioms:  ax-1 3  ax-2 4  ax-3 5  ax-mp 6  ax-6 675

This theorem depends on definitions:  df-bi 128  df-ex 679

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