NFE Home New Foundations Explorer < Previous   Next >
Nearby theorems
Mirrors  >  Home  >  NFE Home  >  Th. List  >  olcd GIF version

Theorem olcd 382
Description: Deduction introducing a disjunct. A translation of natural deduction rule IL ( insertion left), see natded in set.mm. (Contributed by NM, 11-Apr-2008.) (Proof shortened by Wolf Lammen, 3-Oct-2013.)
Hypothesis
Ref Expression
orcd.1 (φψ)
Assertion
Ref Expression
olcd (φ → (χ ψ))

Proof of Theorem olcd
StepHypRef Expression
1 orcd.1 . . 3 (φψ)
21orcd 381 . 2 (φ → (ψ χ))
32orcomd 377 1 (φ → (χ ψ))
Colors of variables: wff setvar class
Syntax hints:  wi 4   wo 357
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8
This theorem depends on definitions:  df-bi 177  df-or 359
This theorem is referenced by:  pm2.48  389  pm2.49  390  orim12i  502  pm1.5  508  nnc0suc  4412  clos1basesuc  5882  nc0le1  6216  frecsuc  6322
  Copyright terms: Public domain W3C validator