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Theorem orim12d 775
Description: Disjoin antecedents and consequents in a deduction. (Contributed by NM, 10-May-1994.)
Hypotheses
Ref Expression
orim12d.1  |-  ( ph  ->  ( ps  ->  ch ) )
orim12d.2  |-  ( ph  ->  ( th  ->  ta ) )
Assertion
Ref Expression
orim12d  |-  ( ph  ->  ( ( ps  \/  th )  ->  ( ch  \/  ta ) ) )

Proof of Theorem orim12d
StepHypRef Expression
1 orim12d.1 . 2  |-  ( ph  ->  ( ps  ->  ch ) )
2 orim12d.2 . 2  |-  ( ph  ->  ( th  ->  ta ) )
3 pm3.48 774 . 2  |-  ( ( ( ps  ->  ch )  /\  ( th  ->  ta ) )  ->  (
( ps  \/  th )  ->  ( ch  \/  ta ) ) )
41, 2, 3syl2anc 408 1  |-  ( ph  ->  ( ( ps  \/  th )  ->  ( ch  \/  ta ) ) )
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  3501  preq12b  3692  prel12  3693  exmidsssnc  4121  funun  5162  nnsucelsuc  6380  nnaord  6398  nnmord  6406  swoer  6450  fidceq  6756  fin0or  6773  enomnilem  7003  exmidomni  7007  fodjuomnilemres  7013  ltsopr  7397  cauappcvgprlemloc  7453  caucvgprlemloc  7476  caucvgprprlemloc  7504  suplocexprlemloc  7522  mulextsr1lem  7581  suplocsrlemb  7607  axpre-suploclemres  7702  reapcotr  8353  apcotr  8362  mulext1  8367  mulext  8369  mul0eqap  8424  peano2z  9083  zeo  9149  uzm1  9349  eluzdc  9397  fzospliti  9946  frec2uzltd  10169  absext  10828  qabsor  10840  maxleast  10978  dvdslelemd  11530  odd2np1lem  11558  odd2np1  11559  isprm6  11814  ennnfonelemrnh  11918  dedekindeulemloc  12755  suplociccreex  12760  dedekindicclemloc  12764  ivthinclemloc  12777  uzdcinzz  12994  bj-findis  13166  nninfomnilem  13203  isomninnlem  13214
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