Theorem imori 428

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 427	. 2 ⊢ ((𝜑 → 𝜓) ↔ (¬ 𝜑 ∨ 𝜓))
3	1, 2	mpbi 220	1 ⊢ (¬ 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 197  df-or 384

This theorem is referenced by:  pm2.1  432  pm2.26  963  rb-ax1  1826  numclwwlk3lemOLD  27550  meran1  32716  meran2  32717  meran3  32718  tsim3  34252  tsor2  34268  tsor3  34269  spr0nelg  42236