Theorem tsim3

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

	Ref	Expression
Assertion	tsim3	⊢ ( 𝜃 → ( ¬ 𝜓 ∨ ( 𝜑 → 𝜓 ) ) )

Proof

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