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Metamath Proof Explorer

Theorem pm4.63

Description: Theorem *4.63 of WhiteheadRussell p. 120. (Contributed by NM, 3-Jan-2005)

Ref Expression
Assertion pm4.63 ( ¬ ( 𝜑 → ¬ 𝜓 ) ↔ ( 𝜑 ∧ 𝜓 ) )

Proof

Step Hyp Ref Expression
1 df-an ⊢ ( ( 𝜑 ∧ 𝜓 ) ↔ ¬ ( 𝜑 → ¬ 𝜓 ) )
2 1 bicomi ⊢ ( ¬ ( 𝜑 → ¬ 𝜓 ) ↔ ( 𝜑 ∧ 𝜓 ) )