Theorem tsim3 38822

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 868	. 2 ⊢ (¬ 𝜓 ∨ (𝜑 → 𝜓))
3	2	a1i 11	1 ⊢ (𝜃 → (¬ 𝜓 ∨ (𝜑 → 𝜓)))

This proof depends on syntax axioms:  ¬ wn 3   → wi 4   ∨ wo 861

This proof depends on axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8

This proof depends on definitions:  df-bi 210  df-or 862

This theorem is used by:  mpobi123f  38852  mptbi12f  38856  ac6s6  38862