Theorem impor

Description: An equivalent formula for implying a disjunction. (Contributed by Giovanni Mascellani, 15-Sep-2017)

	Ref	Expression
Assertion	impor	⊢ ( ( 𝜑 → ( 𝜓 ∨ 𝜒 ) ) ↔ ( ( ¬ 𝜑 ∨ 𝜓 ) ∨ 𝜒 ) )

Proof

Step	Hyp	Ref	Expression
1		imor	⊢ ( ( 𝜑 → ( 𝜓 ∨ 𝜒 ) ) ↔ ( ¬ 𝜑 ∨ ( 𝜓 ∨ 𝜒 ) ) )
2		orass	⊢ ( ( ( ¬ 𝜑 ∨ 𝜓 ) ∨ 𝜒 ) ↔ ( ¬ 𝜑 ∨ ( 𝜓 ∨ 𝜒 ) ) )
3	1 2	bitr4i	⊢ ( ( 𝜑 → ( 𝜓 ∨ 𝜒 ) ) ↔ ( ( ¬ 𝜑 ∨ 𝜓 ) ∨ 𝜒 ) )