ILE Home Intuitionistic Logic Explorer < Previous   Next >
Nearby theorems
Mirrors  >  Home  >  ILE Home  >  Th. List  >  3adant2r Unicode version

Theorem 3adant2r 1233
Description: Deduction adding a conjunct to antecedent. (Contributed by NM, 8-Jan-2006.)
Hypothesis
Ref Expression
3adant1l.1  |-  ( (
ph  /\  ps  /\  ch )  ->  th )
Assertion
Ref Expression
3adant2r  |-  ( (
ph  /\  ( ps  /\ 
ta )  /\  ch )  ->  th )

Proof of Theorem 3adant2r
StepHypRef Expression
1 3adant1l.1 . . . 4  |-  ( (
ph  /\  ps  /\  ch )  ->  th )
213com12 1207 . . 3  |-  ( ( ps  /\  ph  /\  ch )  ->  th )
323adant1r 1231 . 2  |-  ( ( ( ps  /\  ta )  /\  ph  /\  ch )  ->  th )
433com12 1207 1  |-  ( (
ph  /\  ( ps  /\ 
ta )  /\  ch )  ->  th )
Colors of variables: wff set class
Syntax hints:    -> wi 4    /\ wa 104    /\ w3a 978
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 106  ax-ia2 107  ax-ia3 108
This theorem depends on definitions:  df-bi 117  df-3an 980
This theorem is referenced by:  caovimo  6064  mulassnqg  7379  prarloc  7498  ltexprlemfl  7604  ltexprlemfu  7606  addasssrg  7751  axaddass  7867
  Copyright terms: Public domain W3C validator