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 ) )