Theorem pm4.44

Description: Theorem *4.44 of WhiteheadRussell p. 119. (Contributed by NM, 3-Jan-2005)

	Ref	Expression
Assertion	pm4.44	⊢ ( 𝜑 ↔ ( 𝜑 ∨ ( 𝜑 ∧ 𝜓 ) ) )

Proof

Step	Hyp	Ref	Expression
1		orc	⊢ ( 𝜑 → ( 𝜑 ∨ ( 𝜑 ∧ 𝜓 ) ) )
2		id	⊢ ( 𝜑 → 𝜑 )
3		simpl	⊢ ( ( 𝜑 ∧ 𝜓 ) → 𝜑 )
4	2 3	jaoi	⊢ ( ( 𝜑 ∨ ( 𝜑 ∧ 𝜓 ) ) → 𝜑 )
5	1 4	impbii	⊢ ( 𝜑 ↔ ( 𝜑 ∨ ( 𝜑 ∧ 𝜓 ) ) )