Theorem imori 402

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 401	. 2 ⊢ ((φ → ψ) ↔ (¬ φ ∨ ψ))
3	1, 2	mpbi 199	1 ⊢ (¬ φ ∨ ψ)

This proof depends on syntax axioms:  ¬ wn 3   → wi 4   ∨ wo 357

This proof depends on axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8

This proof depends on definitions:  df-bi 177  df-or 359

This theorem is used by:  pm2.1  406  pm2.26  853  rb-ax1  1517