ILE Home Intuitionistic Logic Explorer < Previous   Next >
Nearby theorems
Mirrors  >  Home  >  ILE Home  >  Th. List  >  3adant3l Unicode version

Theorem 3adant3l 1170
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
3adant3l  |-  ( (
ph  /\  ps  /\  ( ta  /\  ch ) )  ->  th )

Proof of Theorem 3adant3l
StepHypRef Expression
1 3adant1l.1 . . . 4  |-  ( (
ph  /\  ps  /\  ch )  ->  th )
213com13 1148 . . 3  |-  ( ( ch  /\  ps  /\  ph )  ->  th )
323adant1l 1166 . 2  |-  ( ( ( ta  /\  ch )  /\  ps  /\  ph )  ->  th )
433com13 1148 1  |-  ( (
ph  /\  ps  /\  ( ta  /\  ch ) )  ->  th )
Colors of variables: wff set class
Syntax hints:    -> wi 4    /\ wa 102    /\ w3a 924
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 104  ax-ia2 105  ax-ia3 106
This theorem depends on definitions:  df-bi 115  df-3an 926
This theorem is referenced by:  addassnqg  6920  mulassnqg  6922  prarloc  7041  prmuloc  7104  addasssrg  7281  axaddass  7386
  Copyright terms: Public domain W3C validator