Theorem exnal 721

Description: Theorem 19.14 of [Margaris] p. 90.

Assertion

Ref	Expression
exnal	⊢ (∃x ¬ φ ↔ ¬ ∀xφ)

Proof of Theorem exnal

Step	Hyp	Ref	Expression
1		alex 717	. 2 ⊢ (∀xφ ↔ ¬ ∃x ¬ φ)
2	1	bicon2i 194	1 ⊢ (∃x ¬ φ ↔ ¬ ∀xφ)

Syntax hints:  ¬ wn 1   ↔ wb 127  ∀wal 672  ∃wex 678

This theorem is referenced by:  alexn 726  19.29 752  eqsex 834  cla42gv 1399  nss 1550  nssss 1866  dtru 1889  intirr 2628  zfcndpow 3762

This theorem was proved from axioms:  ax-1 3  ax-2 4  ax-3 5  ax-mp 6  ax-4 673  ax-5 674  ax-gen 677

This theorem depends on definitions:  df-bi 128  df-an 198  df-ex 679

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