ILE Home Intuitionistic Logic Explorer < Previous   Next >
Nearby theorems
Mirrors  >  Home  >  ILE Home  >  Th. List  >  orim1d Unicode version

Theorem orim1d 711
Description: Disjoin antecedents and consequents in a deduction. (Contributed by NM, 23-Apr-1995.)
Hypothesis
Ref Expression
orim1d.1  |-  ( ph  ->  ( ps  ->  ch ) )
Assertion
Ref Expression
orim1d  |-  ( ph  ->  ( ( ps  \/  th )  ->  ( ch  \/  th ) ) )

Proof of Theorem orim1d
StepHypRef Expression
1 orim1d.1 . 2  |-  ( ph  ->  ( ps  ->  ch ) )
2 idd 21 . 2  |-  ( ph  ->  ( th  ->  th )
)
31, 2orim12d 710 1  |-  ( ph  ->  ( ( ps  \/  th )  ->  ( ch  \/  th ) ) )
Colors of variables: wff set class
Syntax hints:    -> wi 4    \/ wo 639
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 103  ax-ia2 104  ax-ia3 105  ax-io 640
This theorem depends on definitions:  df-bi 114
This theorem is referenced by:  pm2.38  727  pm2.73  730  pm2.74  731  pm2.8  734  pm2.82  736  unss1  3140  acexmidlemcase  5535  nn0ge2m1nn  8299
  Copyright terms: Public domain W3C validator