Theorem ord 630

Description: Deduce implication from disjunction. (Contributed by NM, 18-May-1994.) (Revised by Mario Carneiro, 31-Jan-2015.)

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		pm2.53 628	. 2 ⊢ ((ψ ∨ χ) → (¬ ψ → χ))
3	1, 2	syl 14	1 ⊢ (φ → (¬ ψ → χ))

Syntax hints:  ¬ wn 3   → wi 4   ∨ wo 616

This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 99  ax-ia2 100  ax-ia3 101  ax-in2 533  ax-io 617

This theorem depends on definitions:  df-bi 110

This theorem is referenced by:  pm2.8  710  orcanai  825  ax-12  1383  swopo  4017  sotritrieq  4036  suc11g  4219  ordsoexmid  4224  nnsuc  4265  sotri2  4649  nnsucsssuc  5986  nntri2  5988  nntri1  5989  elni2  6174  nlt1pig  6201  bj-peano4  7177