Theorem pm5.61

Description: Theorem *5.61 of WhiteheadRussell p. 125. (Contributed by NM, 3-Jan-2005) (Proof shortened by Wolf Lammen, 30-Jun-2013)

	Ref	Expression
Assertion	pm5.61	⊢ ( ( ( 𝜑 ∨ 𝜓 ) ∧ ¬ 𝜓 ) ↔ ( 𝜑 ∧ ¬ 𝜓 ) )

Proof

Step	Hyp	Ref	Expression
1		orel2	⊢ ( ¬ 𝜓 → ( ( 𝜑 ∨ 𝜓 ) → 𝜑 ) )
2		orc	⊢ ( 𝜑 → ( 𝜑 ∨ 𝜓 ) )
3	1 2	impbid1	⊢ ( ¬ 𝜓 → ( ( 𝜑 ∨ 𝜓 ) ↔ 𝜑 ) )
4	3	pm5.32ri	⊢ ( ( ( 𝜑 ∨ 𝜓 ) ∧ ¬ 𝜓 ) ↔ ( 𝜑 ∧ ¬ 𝜓 ) )