Theorem orri 365

Description: Infer implication from disjunction. (Contributed by NM, 11-Jun-1994.)

Hypothesis

Ref	Expression
orri.1	⊢ (¬ φ → ψ)

Assertion

Ref	Expression
orri	⊢ (φ ∨ ψ)

Proof of Theorem orri

Step	Hyp	Ref	Expression
1		orri.1	. 2 ⊢ (¬ φ → ψ)
2		df-or 359	. 2 ⊢ ((φ ∨ ψ) ↔ (¬ φ → ψ))
3	1, 2	mpbir 200	1 ⊢ (φ ∨ ψ)

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:  orci  379  olci  380  pm2.25  393  exmid  404  pm2.13  407  pm3.12  486  pm5.11  854  pm5.12  855  pm5.14  856  pm5.15  859  pm5.55  867  pm5.54  870  rb-ax2  1518  rb-ax3  1519  rb-ax4  1520  exmo  2249  abvor0  3568  ifeqor  3700