Theorem a6e 989

Description: Abbreviated version of ax-6o 977.

Assertion

Ref	Expression
a6e	⊢ (∃x∀xφ → φ)

Proof of Theorem a6e

Step	Hyp	Ref	Expression
1		df-ex 980	. 2 ⊢ (∃x∀xφ ↔ ¬ ∀x ¬ ∀xφ)
2		ax-6o 977	. 2 ⊢ (¬ ∀x ¬ ∀xφ → φ)
3	1, 2	sylbi 199	1 ⊢ (∃x∀xφ → φ)

Syntax hints:  ¬ wn 2   → wi 3  ∀wal 953  ∃wex 979

This theorem is referenced by:  ax9o 1121

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

This theorem depends on definitions:  df-bi 147  df-ex 980

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