Theorem 2exnexn 1580

Description: Theorem *11.51 in [WhiteheadRussell] p. 164. (Contributed by Andrew Salmon, 24-May-2011.) (Proof shortened by Wolf Lammen, 25-Sep-2014.)

Assertion

Ref	Expression
2exnexn	⊢ (∃x∀yφ ↔ ¬ ∀x∃y ¬ φ)

Proof of Theorem 2exnexn

Step	Hyp	Ref	Expression
1		alexn 1579	. 2 ⊢ (∀x∃y ¬ φ ↔ ¬ ∃x∀yφ)
2	1	con2bii 322	1 ⊢ (∃x∀yφ ↔ ¬ ∀x∃y ¬ φ)

Syntax hints:  ¬ wn 3   ↔ wb 176  ∀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

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

This theorem is referenced by: (None)