Intuitionistic Logic Explorer < Previous   Next > Nearby theorems Mirrors  >  Home  >  ILE Home  >  Th. List  >  orim12d GIF version

Theorem orim12d 775
 Description: Disjoin antecedents and consequents in a deduction. (Contributed by NM, 10-May-1994.)
Hypotheses
Ref Expression
orim12d.1 (𝜑 → (𝜓𝜒))
orim12d.2 (𝜑 → (𝜃𝜏))
Assertion
Ref Expression
orim12d (𝜑 → ((𝜓𝜃) → (𝜒𝜏)))

Proof of Theorem orim12d
StepHypRef Expression
1 orim12d.1 . 2 (𝜑 → (𝜓𝜒))
2 orim12d.2 . 2 (𝜑 → (𝜃𝜏))
3 pm3.48 774 . 2 (((𝜓𝜒) ∧ (𝜃𝜏)) → ((𝜓𝜃) → (𝜒𝜏)))
41, 2, 3syl2anc 408 1 (𝜑 → ((𝜓𝜃) → (𝜒𝜏)))
 Colors of variables: wff set class Syntax hints:   → wi 4   ∨ wo 697 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 105  ax-ia2 106  ax-ia3 107  ax-io 698 This theorem depends on definitions:  df-bi 116 This theorem is referenced by:  orim1d  776  orim2d  777  3orim123d  1298  19.33b2  1608  eqifdc  3506  preq12b  3697  prel12  3698  exmidsssnc  4126  funun  5167  nnsucelsuc  6387  nnaord  6405  nnmord  6413  swoer  6457  fidceq  6763  fin0or  6780  enomnilem  7010  exmidomni  7014  fodjuomnilemres  7020  ltsopr  7411  cauappcvgprlemloc  7467  caucvgprlemloc  7490  caucvgprprlemloc  7518  suplocexprlemloc  7536  mulextsr1lem  7595  suplocsrlemb  7621  axpre-suploclemres  7716  reapcotr  8367  apcotr  8376  mulext1  8381  mulext  8383  mul0eqap  8438  peano2z  9097  zeo  9163  uzm1  9363  eluzdc  9411  fzospliti  9960  frec2uzltd  10183  absext  10842  qabsor  10854  maxleast  10992  dvdslelemd  11548  odd2np1lem  11576  odd2np1  11577  isprm6  11832  ennnfonelemrnh  11936  dedekindeulemloc  12776  suplociccreex  12781  dedekindicclemloc  12785  ivthinclemloc  12798  cos11  12947  uzdcinzz  13035  bj-findis  13207  nninfomnilem  13244  isomninnlem  13255
 Copyright terms: Public domain W3C validator