This is an inofficial mirror of http://metamath.tirix.org for personal testing of a visualizer extension only.

Metamath Proof Explorer

Theorem pm4.55

Description: Theorem *4.55 of WhiteheadRussell p. 120. (Contributed by NM, 3-Jan-2005)

Ref Expression
Assertion pm4.55 ⊢ ¬ ¬ φ ∧ ψ ↔ φ ∨ ¬ ψ

Proof

Step Hyp Ref Expression
1 pm4.54 ⊢ ¬ φ ∧ ψ ↔ ¬ φ ∨ ¬ ψ
2 1 con2bii ⊢ φ ∨ ¬ ψ ↔ ¬ ¬ φ ∧ ψ
3 2 bicomi ⊢ ¬ ¬ φ ∧ ψ ↔ φ ∨ ¬ ψ