Theorem tsim2

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

	Ref	Expression
Assertion	tsim2	⊢ ( 𝜃 → ( 𝜑 ∨ ( 𝜑 → 𝜓 ) ) )

Proof

Step	Hyp	Ref	Expression
1		curryax	⊢ ( 𝜑 ∨ ( 𝜑 → 𝜓 ) )
2	1	a1i	⊢ ( 𝜃 → ( 𝜑 ∨ ( 𝜑 → 𝜓 ) ) )