Theorem tsim3 33109

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 428	. 2 ⊢ (¬ 𝜓 ∨ (𝜑 → 𝜓))
3	2	a1i 11	1 ⊢ (𝜃 → (¬ 𝜓 ∨ (𝜑 → 𝜓)))

Syntax hints:  ¬ wn 3   → wi 4   ∨ wo 382

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 196  df-or 384

This theorem is referenced by:  mpt2bi123f  33141  mptbi12f  33145  ac6s6  33150