Theorem pm4.56 769

Description: Theorem *4.56 of [WhiteheadRussell] p. 120. (Contributed by NM, 3-Jan-2005.)

Assertion

Ref	Expression
pm4.56	⊢ ((¬ 𝜑 ∧ ¬ 𝜓) ↔ ¬ (𝜑 ∨ 𝜓))

Proof of Theorem pm4.56

Step	Hyp	Ref	Expression
1		ioran 741	. 2 ⊢ (¬ (𝜑 ∨ 𝜓) ↔ (¬ 𝜑 ∧ ¬ 𝜓))
2	1	bicomi 131	1 ⊢ ((¬ 𝜑 ∧ ¬ 𝜓) ↔ ¬ (𝜑 ∨ 𝜓))

Syntax hints:  ¬ wn 3   ∧ wa 103   ↔ wb 104   ∨ wo 697

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 105  ax-ia2 106  ax-ia3 107  ax-in1 603  ax-in2 604  ax-io 698

This theorem depends on definitions:  df-bi 116

This theorem is referenced by:  oranim  770  orandc  923  neanior  2393  prneimg  3696  nqnq0pi  7239