Theorem a6e 1751

Description: Abbreviated version of ax6o 1750. (Contributed by NM, 5-Aug-1993.)

Assertion

Ref	Expression
a6e	⊢ (∃x∀xφ → φ)

Proof of Theorem a6e

Step	Hyp	Ref	Expression
1		df-ex 1542	. 2 ⊢ (∃x∀xφ ↔ ¬ ∀x ¬ ∀xφ)
2		ax6o 1750	. 2 ⊢ (¬ ∀x ¬ ∀xφ → φ)
3	1, 2	sylbi 187	1 ⊢ (∃x∀xφ → φ)

Syntax hints:  ¬ wn 3   → wi 4  ∀wal 1540  ∃wex 1541

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-17 1616  ax-9 1654  ax-8 1675  ax-6 1729  ax-11 1746

This theorem depends on definitions:  df-bi 177  df-ex 1542

This theorem is referenced by: (None)