ILE Home Intuitionistic Logic Explorer < Previous   Next >
Nearby theorems
Mirrors  >  Home  >  ILE Home  >  Th. List  >  orim1i Unicode version

Theorem orim1i 755
Description: Introduce disjunct to both sides of an implication. (Contributed by NM, 6-Jun-1994.)
Hypothesis
Ref Expression
orim1i.1  |-  ( ph  ->  ps )
Assertion
Ref Expression
orim1i  |-  ( (
ph  \/  ch )  ->  ( ps  \/  ch ) )

Proof of Theorem orim1i
StepHypRef Expression
1 orim1i.1 . 2  |-  ( ph  ->  ps )
2 id 19 . 2  |-  ( ch 
->  ch )
31, 2orim12i 754 1  |-  ( (
ph  \/  ch )  ->  ( ps  \/  ch ) )
Colors of variables: wff set class
Syntax hints:    -> wi 4    \/ wo 703
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 704
This theorem depends on definitions:  df-bi 116
This theorem is referenced by:  19.34  1677  dveeq2or  1809  sbequilem  1831  sbequi  1832  dvelimALT  2003  dvelimfv  2004  dvelimor  2011  r19.45av  2630  acexmidlemcase  5845  omniwomnimkv  7139  nnm1nn0  9163  prmdc  12071  triap  14021
  Copyright terms: Public domain W3C validator