Theorem imori 855

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 854	. 2 ⊢ ((𝜑 → 𝜓) ↔ (¬ 𝜑 ∨ 𝜓))
3	1, 2	mpbi 230	1 ⊢ (¬ 𝜑 ∨ 𝜓)

Syntax hints:  ¬ wn 3   → wi 4   ∨ wo 848

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 849

This theorem is referenced by:  pm2.1  897  pm2.26  942  rb-ax1  1752  fmla0disjsuc  35403  nrmo  36411  meran1  36412  meran2  36413  meran3  36414  tsim3  38139  tsor2  38155  tsor3  38156  spr0nelg  47463