ILE Home Intuitionistic Logic Explorer < Previous   Next >
Nearby theorems
Mirrors  >  Home  >  ILE Home  >  Th. List  >  3adant1l Unicode version

Theorem 3adant1l 1208
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
3adant1l  |-  ( ( ( ta  /\  ph )  /\  ps  /\  ch )  ->  th )

Proof of Theorem 3adant1l
StepHypRef Expression
1 3adant1l.1 . . . 4  |-  ( (
ph  /\  ps  /\  ch )  ->  th )
213expb 1182 . . 3  |-  ( (
ph  /\  ( ps  /\ 
ch ) )  ->  th )
32adantll 467 . 2  |-  ( ( ( ta  /\  ph )  /\  ( ps  /\  ch ) )  ->  th )
433impb 1177 1  |-  ( ( ( ta  /\  ph )  /\  ps  /\  ch )  ->  th )
Colors of variables: wff set class
Syntax hints:    -> wi 4    /\ wa 103    /\ w3a 962
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 105  ax-ia2 106  ax-ia3 107
This theorem depends on definitions:  df-bi 116  df-3an 964
This theorem is referenced by:  3adant2l  1210  3adant3l  1212  tfrcl  6254  addassnqg  7183  mulassnqg  7185  addasssrg  7557  axaddass  7673
  Copyright terms: Public domain W3C validator