Theorem imori 860

Description: Infer disjunction from implication. (Contributed by NM, 12-Mar-2012.)

Hypothesis

Ref	Expression
imori.1	⊢ (𝜑 → 𝜓)

Assertion

Ref	Expression
imori	⊢ (¬ 𝜑 ∨ 𝜓)

Proof of Theorem imori

Step	Hyp	Ref	Expression
1		imori.1	. 2 ⊢ (𝜑 → 𝜓)
2		imor 859	. 2 ⊢ ((𝜑 → 𝜓) ↔ (¬ 𝜑 ∨ 𝜓))
3	1, 2	mpbi 231	1 ⊢ (¬ 𝜑 ∨ 𝜓)

Syntax hints:  ¬ wn 3   → wi 4   ∨ wo 853

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 208  df-or 854

This theorem is referenced by:  pm2.1  902  pm2.26  947  rb-ax1  1759  fmla0disjsuc  35633  nrmo  36645  meran1  36646  meran2  36647  meran3  36648  tsim3  38506  tsor2  38522  tsor3  38523  spr0nelg  47958  pg4cyclnex  48625