Theorem pm5.62

Description: Theorem *5.62 of WhiteheadRussell p. 125. (Contributed by Roy F. Longton, 21-Jun-2005)

	Ref	Expression
Assertion	pm5.62	⊢ ( ( ( 𝜑 ∧ 𝜓 ) ∨ ¬ 𝜓 ) ↔ ( 𝜑 ∨ ¬ 𝜓 ) )

Proof

Step	Hyp	Ref	Expression
1		exmid	⊢ ( 𝜓 ∨ ¬ 𝜓 )
2		ordir	⊢ ( ( ( 𝜑 ∧ 𝜓 ) ∨ ¬ 𝜓 ) ↔ ( ( 𝜑 ∨ ¬ 𝜓 ) ∧ ( 𝜓 ∨ ¬ 𝜓 ) ) )
3	1 2	mpbiran2	⊢ ( ( ( 𝜑 ∧ 𝜓 ) ∨ ¬ 𝜓 ) ↔ ( 𝜑 ∨ ¬ 𝜓 ) )