Theorem orcanai 879

Description: Change disjunction in consequent to conjunction in antecedent. (Contributed by NM, 8-Jun-1994.)

Hypothesis

Ref	Expression
orcanai.1	⊢ (φ → (ψ ∨ χ))

Assertion

Ref	Expression
orcanai	⊢ ((φ ∧ ¬ ψ) → χ)

Proof of Theorem orcanai

Step	Hyp	Ref	Expression
1		orcanai.1	. . 3 ⊢ (φ → (ψ ∨ χ))
2	1	ord 366	. 2 ⊢ (φ → (¬ ψ → χ))
3	2	imp 418	1 ⊢ ((φ ∧ ¬ ψ) → χ)

Syntax hints:  ¬ wn 3   → wi 4   ∨ wo 357   ∧ wa 358

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 177  df-or 359  df-an 360

This theorem is referenced by: (None)