Theorem tsor2 38172

Description: A Tseitin axiom for logical disjunction, in deduction form. (Contributed by Giovanni Mascellani, 25-Mar-2018.)

Assertion

Ref	Expression
tsor2	⊢ (𝜃 → (¬ 𝜑 ∨ (𝜑 ∨ 𝜓)))

Proof of Theorem tsor2

Step	Hyp	Ref	Expression
1		orc 867	. . 3 ⊢ (𝜑 → (𝜑 ∨ 𝜓))
2	1	imori 854	. 2 ⊢ (¬ 𝜑 ∨ (𝜑 ∨ 𝜓))
3	2	a1i 11	1 ⊢ (𝜃 → (¬ 𝜑 ∨ (𝜑 ∨ 𝜓)))

Syntax hints:  ¬ wn 3   → wi 4   ∨ wo 847

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 207  df-or 848

This theorem is referenced by:  ts3or2  38178