Theorem tsor3

Description: A Tseitin axiom for logical disjunction, in deduction form. (Contributed by Giovanni Mascellani, 25-Mar-2018)

	Ref	Expression
Assertion	tsor3	⊢ ( 𝜃 → ( ¬ 𝜓 ∨ ( 𝜑 ∨ 𝜓 ) ) )

Proof

Step	Hyp	Ref	Expression
1		olc	⊢ ( 𝜓 → ( 𝜑 ∨ 𝜓 ) )
2	1	imori	⊢ ( ¬ 𝜓 ∨ ( 𝜑 ∨ 𝜓 ) )
3	2	a1i	⊢ ( 𝜃 → ( ¬ 𝜓 ∨ ( 𝜑 ∨ 𝜓 ) ) )