Theorem orcanai 515

Description: Change disjunction in consequent to conjunction in antecedent.

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 202	. 2 ⊢ (φ → (¬ ψ → χ))
3	2	imp 277	1 ⊢ ((φ ∧ ¬ ψ) → χ)

Syntax hints:  ¬ wn 1   → wi 2   ∨ wo 195   ∧ wa 196

This theorem is referenced by:  dflim3 2368  bren2 3293  php 3409

This theorem was proved from axioms:  ax-1 3  ax-2 4  ax-3 5  ax-mp 6

This theorem depends on definitions:  df-bi 128  df-or 197  df-an 198

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