Metamath Proof Explorer

Theorem pm4.53

Description: Theorem *4.53 of WhiteheadRussell p. 120. (Contributed by NM, 3-Jan-2005)

Ref Expression
Assertion pm4.53 ( ¬ ( 𝜑 ∧ ¬ 𝜓 ) ↔ ( ¬ 𝜑 ∨ 𝜓 ) )

Proof

Step Hyp Ref Expression
1 pm4.52 ⊢ ( ( 𝜑 ∧ ¬ 𝜓 ) ↔ ¬ ( ¬ 𝜑 ∨ 𝜓 ) )
2 1 con2bii ⊢ ( ( ¬ 𝜑 ∨ 𝜓 ) ↔ ¬ ( 𝜑 ∧ ¬ 𝜓 ) )
3 2 bicomi ⊢ ( ¬ ( 𝜑 ∧ ¬ 𝜓 ) ↔ ( ¬ 𝜑 ∨ 𝜓 ) )