Theorem orrd 367

Description: Deduce implication from disjunction. (Contributed by NM, 27-Nov-1995.)

Hypothesis

Ref	Expression
orrd.1	⊢ (φ → (¬ ψ → χ))

Assertion

Ref	Expression
orrd	⊢ (φ → (ψ ∨ χ))

Proof of Theorem orrd

Step	Hyp	Ref	Expression
1		orrd.1	. 2 ⊢ (φ → (¬ ψ → χ))
2		pm2.54 363	. 2 ⊢ ((¬ ψ → χ) → (ψ ∨ χ))
3	1, 2	syl 15	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:  olc  373  orc  374  pm2.68  399  pm4.79  566  sspss  3369  pwpw0  3856  sssn  3865  pwsnALT  3883  unissint  3951  pwadjoin  4120  nndisjeq  4430  xpexr  5110  fvclss  5463  erdisj  5973