Theorem pm4.43

Description: Theorem *4.43 of WhiteheadRussell p. 119. (Contributed by NM, 3-Jan-2005) (Proof shortened by Wolf Lammen, 26-Nov-2012)

	Ref	Expression
Assertion	pm4.43	⊢ ( 𝜑 ↔ ( ( 𝜑 ∨ 𝜓 ) ∧ ( 𝜑 ∨ ¬ 𝜓 ) ) )

Proof

Step	Hyp	Ref	Expression
1		pm3.24	⊢ ¬ ( 𝜓 ∧ ¬ 𝜓 )
2	1	biorfi	⊢ ( 𝜑 ↔ ( 𝜑 ∨ ( 𝜓 ∧ ¬ 𝜓 ) ) )
3		ordi	⊢ ( ( 𝜑 ∨ ( 𝜓 ∧ ¬ 𝜓 ) ) ↔ ( ( 𝜑 ∨ 𝜓 ) ∧ ( 𝜑 ∨ ¬ 𝜓 ) ) )
4	2 3	bitri	⊢ ( 𝜑 ↔ ( ( 𝜑 ∨ 𝜓 ) ∧ ( 𝜑 ∨ ¬ 𝜓 ) ) )