Theorem tsan1

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

	Ref	Expression
Assertion	tsan1	⊢ ( 𝜃 → ( ( ¬ 𝜑 ∨ ¬ 𝜓 ) ∨ ( 𝜑 ∧ 𝜓 ) ) )

Proof

Step	Hyp	Ref	Expression
1		pm3.12	⊢ ( ( ¬ 𝜑 ∨ ¬ 𝜓 ) ∨ ( 𝜑 ∧ 𝜓 ) )
2	1	a1i	⊢ ( 𝜃 → ( ( ¬ 𝜑 ∨ ¬ 𝜓 ) ∨ ( 𝜑 ∧ 𝜓 ) ) )