Theorem tsim2 36289

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

Assertion

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

Proof of Theorem tsim2

Step	Hyp	Ref	Expression
1		curryax 891	. 2 ⊢ (𝜑 ∨ (𝜑 → 𝜓))
2	1	a1i 11	1 ⊢ (𝜃 → (𝜑 ∨ (𝜑 → 𝜓)))

Syntax hints:   → wi 4   ∨ wo 844

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8

This theorem depends on definitions:  df-bi 206  df-or 845

This theorem is referenced by:  mpobi123f  36320  ac6s6  36330