Theorem tsim3 35412

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

Assertion

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

Proof of Theorem tsim3

Step	Hyp	Ref	Expression
1		ax-1 6	. . 3 ⊢ (𝜓 → (𝜑 → 𝜓))
2	1	imori 850	. 2 ⊢ (¬ 𝜓 ∨ (𝜑 → 𝜓))
3	2	a1i 11	1 ⊢ (𝜃 → (¬ 𝜓 ∨ (𝜑 → 𝜓)))

Syntax hints:  ¬ wn 3   → wi 4   ∨ wo 843

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 209  df-or 844

This theorem is referenced by:  mpobi123f  35442  mptbi12f  35446  ac6s6  35452