Theorem qexmid 1886

Description: Quantified "excluded middle." Exercise 9.2a of Boolos, p. 111, Computability and Logic. (Contributed by NM, 10-Dec-2000.)

Assertion

Ref	Expression
qexmid	⊢ ∃x(φ → ∀xφ)

Proof of Theorem qexmid

Step	Hyp	Ref	Expression
1		19.8a 1756	. 2 ⊢ (∀xφ → ∃x∀xφ)
2	1	19.35ri 1602	1 ⊢ ∃x(φ → ∀xφ)

Syntax hints:   → 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-11 1746

This theorem depends on definitions:  df-bi 177  df-an 360  df-ex 1542

This theorem is referenced by: (None)