Theorem ord 366

Description: Deduce implication from disjunction. (Contributed by NM, 18-May-1994.)

Hypothesis

Ref	Expression
ord.1	⊢ (φ → (ψ ∨ χ))

Assertion

Ref	Expression
ord	⊢ (φ → (¬ ψ → χ))

Proof of Theorem ord

Step	Hyp	Ref	Expression
1		ord.1	. 2 ⊢ (φ → (ψ ∨ χ))
2		df-or 359	. 2 ⊢ ((ψ ∨ χ) ↔ (¬ ψ → χ))
3	1, 2	sylib 188	1 ⊢ (φ → (¬ ψ → χ))

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

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

This theorem is referenced by:  orcanai  879  oplem1  930  ecase23d  1285  19.33b  1608  eqsn  3868  nnsucelr  4429  lenltfin  4470  vfin1cltv  4548  phi011lem1  4599  foconst  5281  nceleq  6150  addceq0  6220  ncslemuc  6256  nchoicelem8  6297