Theorem tsan3

Description: A Tseitin axiom for logical conjunction, in deduction form. (Contributed by Giovanni Mascellani, 24-Mar-2018)

	Ref	Expression
Assertion	tsan3	⊢ ( 𝜃 → ( 𝜓 ∨ ¬ ( 𝜑 ∧ 𝜓 ) ) )

Proof

Step	Hyp	Ref	Expression
1		pm3.14	⊢ ( ( ¬ 𝜑 ∨ ¬ 𝜓 ) → ¬ ( 𝜑 ∧ 𝜓 ) )
2	1	olcs	⊢ ( ¬ 𝜓 → ¬ ( 𝜑 ∧ 𝜓 ) )
3	2	orri	⊢ ( 𝜓 ∨ ¬ ( 𝜑 ∧ 𝜓 ) )
4	3	a1i	⊢ ( 𝜃 → ( 𝜓 ∨ ¬ ( 𝜑 ∧ 𝜓 ) ) )